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2395
Jauslin_2022.tex Normal file
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Makefile Normal file
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PROJECTNAME=$(basename $(wildcard *.tex))
LIBS=$(notdir $(wildcard libs/*))
FIGS=$(notdir $(wildcard figs/*.fig))
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME))
all: $(PROJECTNAME)
$(PROJECTNAME): $(LIBS) $(FIGS)
pdflatex -file-line-error $@.tex
pdflatex -file-line-error $@.tex
pdflatex -synctex=1 $@.tex
$(PROJECTNAME).aux: $(LIBS) $(FIGS)
pdflatex -file-line-error -draftmode $(PROJECTNAME).tex
$(SYNCTEXS): $(LIBS) $(FIGS)
pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@)
libs: $(LIBS)
$(LIBS):
ln -fs libs/$@ ./
bibliography/bibliography.tex: $(PROJECTNAME).aux
BBlog -c bibliography/conf.BBlog -d $(BIBLIOGRAPHY) -b bibliography/bibliography.tex
figs: $(FIGS)
$(FIGS):
make -C figs/$@
for pdf in $$(find figs/$@/ -name '*.pdf'); do ln -fs "$$pdf" ./ ; done
clean-aux: clean-figs-aux
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
rm -f $(addsuffix .out, $(PROJECTNAME))
rm -f $(addsuffix .toc, $(PROJECTNAME))
clean-libs:
rm -f $(LIBS)
clean-figs:
$(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean clean-dat; )
rm -f $(notdir $(wildcard figs/*.fig/*.pdf))
clean-figs-aux:
$(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean-aux; )
clean-tex:
rm -f $(PDFS) $(SYNCTEXS)
clean-bibliography:
rm -f bibliography/bibliography.tex
clean: clean-aux clean-tex clean-libs clean-figs

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README Normal file
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This directory contains the source files to typeset the article, and generate
the figures. This can be accomplished by running
make
This document uses a custom class file, located in the 'libs' directory, which
defines a number of commands. Most of these are drop-in replacements for those
defined in the 'article' class.
Some extra functionality is provided in custom style files, located in the
'libs' directory.
* Dependencies:
pdflatex
TeXlive packages:
amsfonts
array
color
graphics
hyperref
latex
marginnote
mathds
pgf
standalone
GNU make
gnuplot
meankondo v1.5
* Files:
Jauslin_2022.tex:
main LaTeX file
libs:
custom LaTeX class file
figs:
source code for the figures

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bibliography/bibliography.tex Normal file
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\bibitem[An70]{An70}P.W. Anderson - {\it A poor man's derivation of scaling laws for the Kondo problem}, Journal of Physics C: Solid State Physics, volume\-~3, page\-~2436, 1970,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1088/0022-3719/3/12/008}{10.1088/0022-3719/3/12/008}}.\par\medskip
\bibitem[An80]{An80}N. Andrei - {\it Diagonalization of the Kondo Hamiltonian}, Physical Review Letters, volume\-~45, issue\-~5, 1980,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevLett.45.379}{10.1103/PhysRevLett.45.379}}.\par\medskip
\bibitem[BF84]{BF84}G.A. Battle, P. Federbush - {\it A note on cluster expansions, tree graph identities, extra $1/N!$ factors!!!}, Letters in Mathematical Physics, volume\-~8, pages\-~55-57, 1984,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/BF00420041}{10.1007/BF00420041}}.\par\medskip
\bibitem[BCe78]{BCe78}G. Benfatto, M. Cassandro, G. Gallavotti, F. Nicol\`o, E. Olivieri, E. Presutti, E. Scacciatelli - {\it Some probabilistic techniques in field theory}, Communications in Mathematical Physics, volume\-~59, issue\-~2, pages\-~143-166, 1978,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/BF01614247}{10.1007/BF01614247}}.\par\medskip
\bibitem[BG90]{BG90}G. Benfatto, G. Gallavotti - {\it Perturbation theory of the Fermi surface in a quantum liquid - a general quasiparticle formalism and one-dimensional systems}, Journal of Statistical Physics, volume\-~59, issue\-~3-4, pages\-~541-664, 1990,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/BF01025844}{10.1007/BF01025844}}.\par\medskip
\bibitem[BGe94]{BGe94}G. Benfatto, G. Gallavotti, A.Procacci, B. Scoppola - {\it Beta function and Schwinger functions for a many Fermions system in one dimension - Anomaly of the Fermi surface}, Communications in Mathematical Physics, volume\-~160, pages\-~93-171, 1994,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/BF02099791}{10.1007/BF02099791}}.\par\medskip
\bibitem[BGJ15]{BGJ15}G. Benfatto, G. Gallavotti, I. Jauslin - {\it Kondo Effect in a Fermionic Hierarchical Model}, Journal of Statistical Physics, volume\-~161, issue\-~5, pages\-~1203-1230, 2015,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s10955-015-1378-7}{10.1007/s10955-015-1378-7}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1506.04381}{1506.04381}}.\par\medskip
\bibitem[BF78]{BF78}D. Brydges, P. Federbush - {\it A new form of the Mayer expansion in classical statistical mechanics}, Journal of Mathematical Physics, volume\-~19, page\-~2064, 1978,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1063/1.523586}{10.1063/1.523586}}.\par\medskip
\bibitem[Do91]{Do91}T.C. Dorlas - {\it Renormalization group analysis of a simple hierarchical fermion model}, Communications in Mathematical Physics, volume\-~136, pages\-~169-194, 1991,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/BF02096796}{10.1007/BF02096796}}.\par\medskip
\bibitem[Dy69]{Dy69}F.J. Dyson - {\it Existence of a phase-transition in a one-dimensional Ising ferromagnet}, Communications in Mathematical Physics, volume\-~12, pages\-~91-107, 1969,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/BF01645907}{10.1007/BF01645907}}.\par\medskip
\bibitem[GJ15]{GJ15}G. Gallavotti, I. Jauslin - {\it Kondo Effect in the Hierarchical s-d Model}, Journal of Statistical Physics, volume\-~161, issue\-~5, pages\-~1231-1235, 2015,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s10955-015-1370-2}{10.1007/s10955-015-1370-2}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1507.05678}{1507.05678}}.\par\medskip
\bibitem[GN85]{GN85}G. Gallavotti, F. Nicol\`o - {\it Renormalization theory for four dimensional scalar fields I}, Communications in Mathematical Physics, volume\-~100, pages\-~545-590, 1985,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/BF01217729}{10.1007/BF01217729}}.\par\medskip
\bibitem[GK81]{GK81}K. Gawedzki, A. Kupiainen - {\it Renormalization group study of a critical lattice model I: Convergence to the line of fixed points}, Communications in Mathematical Physics, volume\-~82, issue\-~3, pages\-~407-433, 1981,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/BF01237048}{10.1007/BF01237048}}.\par\medskip
\bibitem[Gi10]{Gi10}A. Giuliani - {\it The Ground State Construction of the Two-dimensional Hubbard Model on the Honeycomb Lattice}, Quantum Theory from Small to Large Scales, lecture notes of the Les Houches Summer School, volume\-~95, Oxford University Press, 2010, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1102.3881}{1102.3881}}.\par\medskip
\bibitem[GGM12]{GGM12}A. Giuliani, R.L. Greenblatt, V. Mastropietro - {\it The scaling limit of the energy correlations in non-integrable Ising models}, Journal of Mathematical Physics, volume\-~53, page\-~095214, 2012,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1063/1.4745910}{10.1063/1.4745910}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1204.4040}{1204.4040}}.\par\medskip
\bibitem[GJ16]{GJ16}A. Giuliani, I. Jauslin - {\it The ground state construction of bilayer graphene}, Reviews in Mathematical Physics, volume\-~28, issue\-~8, page\-~1650018, 2016,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1142/S0129055X16500185}{10.1142/S0129055X16500185}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1507.06024}{1507.06024}}.\par\medskip
\bibitem[GM10]{GM10}A. Giuliani, V. Mastropietro - {\it The two-dimensional Hubbard model on the honeycomb lattice}, Communications in Mathematical Physics, volume\-~293, pages\-~301-364, 2010,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s00220-009-0910-5}{10.1007/s00220-009-0910-5}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/0811.1881}{0811.1881}}.\par\medskip
\bibitem[GMP12]{GMP12}A. Giuliani, V. Mastropietro, M. Porta - {\it Universality of conductivity in interacting graphene}, Communications in Mathematical Physics, volume\-~311, issue\-~2, pages\-~317-355, 2012,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s00220-012-1444-9}{10.1007/s00220-012-1444-9}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1101.2169}{1101.2169}}.\par\medskip
\bibitem[GMP17]{GMP17}A. Giuliani, V. Mastropietro, M. Porta - {\it Universality of the Hall Conductivity in Interacting Electron Systems}, Communications in Mathematical Physics, volume\-~349, issue\-~3, pages\-~1107-1161, 2017,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s00220-016-2714-8}{10.1007/s00220-016-2714-8}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1511.04047}{1511.04047}}.\par\medskip
\bibitem[Ko64]{Ko64}J. Kondo - {\it Resistance minimum in dilute magnetic alloys}, Progress of Theoretical Physics, volume\-~32, issue\-~1, 1964,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1143/PTP.32.37}{10.1143/PTP.32.37}}.\par\medskip
\bibitem[Ma11]{Ma11}V. Mastropietro - {\it Conductivity between Luttinger liquids: coupled chains and bilayer graphene}, Physical Review B, volume\-~84, page\-~035109, 2011,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevB.84.035109}{10.1103/PhysRevB.84.035109}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1012.5736}{1012.5736}}.\par\medskip
\bibitem[Mc57]{Mc57}J.W. McClure - {\it Band structure of graphite and de Haas-van Alphen effect}, Physical review, volume\-~108, pages\-~612-618, 1957,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.108.612}{10.1103/PhysRev.108.612}}.\par\medskip
\bibitem[NGe04]{NGe04}K.S. Novoselov, A.K. Geim, S. V.Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov - {\it Electric field effect in atomically thin carbon films}, Science, vol. 306, pages\-~666-669, 2004,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1126/science.1102896}{10.1126/science.1102896}}.\par\medskip
\bibitem[SW58]{SW58}J.C. Slonczewski, P.R. Weiss - {\it Band structure of graphite}, Physical Review, volume\-~109, pages\-~272-279, 1958,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.109.272}{10.1103/PhysRev.109.272}}.\par\medskip
\bibitem[Wi65]{Wi65}K.G. Wilson - {\it Model Hamiltonians for Local Quantum Field Theory}, Physical Review, volume\-~140, issue\-~2B, page B445-B457, 1965,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.140.B445}{10.1103/PhysRev.140.B445}}.\par\medskip
\bibitem[Wi75]{Wi75}K.G. Wilson - {\it The renormalization group: Critical phenomena and the Kondo problem}, Reviews of Modern Physics, volume\-~47, issue\-~4, 1975,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/RevModPhys.47.773}{10.1103/RevModPhys.47.773}}.\par\medskip
\bibitem[mk]{mk}{\tt meankondo} software package v1.5, I.\-~Jauslin,\par\penalty10000
{\tt\color{blue}\href{http://ian.jauslin.org/software/meankondo}{http://ian.jauslin.org/software/meankondo}}.\par\medskip

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figs/bands.fig/Makefile Normal file
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PROJECTNAME=$(basename $(wildcard *.gnuplot))
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
all: $(PDFS)
$(PDFS):
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
install: $(PDFS)
cp $^ $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
clean-dat:
rm -f $(DATS)
clean-tex:
rm -f $(PDFS)
clean: clean-aux clean-tex

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figs/bands.fig/bands.gnuplot Normal file
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# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 8,6 standalone
unset key
unset xtics
unset ytics
unset ztics
unset border
unset colorbox
set pointsize 1
#set xrange [0:4*pi/3]
#set yrange [-2*pi/sqrt(3):2*pi/sqrt(3)]
set pm3d depthorder
# make this odd and divisible by 7 to get the Fermi points
set isosamples 49
# rescale x and y components to render the Fermi points better
# units of 2*pi/3
set xrange [0:2]
# units of 2*pi/(3*sqrt(3))
set yrange [-3:3]
set view 80,35
splot sqrt(1+4*cos(pi*x)*cos(pi/3*y)+4*cos(pi/3*y)**2) w pm3d, -sqrt(1+4*cos(pi*x)*cos(pi/3*y)+4*cos(pi/3*y)**2) w pm3d
#pause mouse close

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figs/bilayer.fig/Makefile Normal file
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PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex)))
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
all: $(PDFS)
$(PDFS):
pdflatex -jobname $(basename $@) $(patsubst %.pdf, %.tikz.tex, $@)
install: $(PROJECTNAME)
cp $^.pdf $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
rm -f $(addsuffix .out, $(PROJECTNAME))
clean-tex:
rm -f $(PDFS) $(SYNCTEXS)
clean: clean-aux clean-tex

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figs/bilayer.fig/bilayer.tikz.tex Normal file
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\documentclass{standalone}
\usepackage{tikz}
\usepackage{graphene}
% reflected graphene grid at #1 of width #2 and height #3
\def\graphenereflected#1#2#3{
\foreach \i in {0,...,#2}{
\foreach \j in {0,...,#3}{
\cellreflected{#1++(\i*3,-2*\j*\sqrtThOT)}
\cellreflected{#1++(\i*3+1.5,\sqrtThOT-2*\j*\sqrtThOT)}
}
}
}
\def\cellreflected#1{
\draw[dotted]#1--++(0:-1);
\draw[dotted]#1--++(120:-1);
\draw[dotted]#1--++(240:-1);
\asite{#1}
\draw[dotted]#1++(-1,0)--++(0:1);
\draw[dotted]#1++(-1,0)--++(120:1);
\draw[dotted]#1++(-1,0)--++(240:1);
\bsite{#1++(-1,0)}
}
\def\square#1#2{\draw#1++(-#2,-#2)--++(#2,0)--++(#2,0)--++(0,#2)--++(0,#2)--++(-#2,0)--++(-#2,0)--++(0,-#2)--++(0,-#2);}
\begin{document}
\begin{tikzpicture}
% first layer
\graphene{(0,0)}{3}{3}
% redefine sites for second layer
\def\bsite#1{\draw#1circle(.1);}
\def\asite#1{\square{#1}{.17}}
% second layer
\graphenereflected{(0,0)}{3}{3}
\end{tikzpicture}
\end{document}

1
figs/bilayer.fig/graphene.sty Symbolic link
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../lib/graphene.sty

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figs/brillouin.fig/Makefile Normal file
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PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex)))
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
all: $(PDFS)
$(PDFS):
pdflatex -jobname $(basename $@) $(patsubst %.pdf, %.tikz.tex, $@)
install: $(PROJECTNAME)
cp $^.pdf $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
rm -f $(addsuffix .out, $(PROJECTNAME))
clean-tex:
rm -f $(PDFS) $(SYNCTEXS)
clean: clean-aux clean-tex

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figs/brillouin.fig/brillouin.tikz.tex Normal file
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\documentclass{standalone}
\usepackage{tikz}
% sqrt(3)
\def\sqrtTh{1.732}
% pi
\def\pival{3.14159}
\begin{document}
\begin{tikzpicture}
\draw(0,0)--(2*\pival/3,2*\pival/\sqrtTh)--(4*\pival/3,0)--(2*\pival/3,-2*\pival/\sqrtTh)--cycle;
\fill(2*\pival/3,2*\pival/3/\sqrtTh)circle(0.05);
\fill(2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.05);
\end{tikzpicture}
\end{document}

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figs/brillouin.fig/scales.tikz.tex Normal file
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\documentclass{standalone}
\usepackage{tikz}
\usepackage{xcolor}
\definecolor{gray0}{HTML}{EEEEEE}
\definecolor{gray1}{HTML}{CCCCCC}
\definecolor{gray2}{HTML}{AAAAAA}
\definecolor{gray3}{HTML}{888888}
\definecolor{gray4}{HTML}{666666}
\definecolor{gray5}{HTML}{444444}
\definecolor{gray6}{HTML}{222222}
\definecolor{gray7}{HTML}{000000}
% sqrt(3)
\def\sqrtTh{1.732}
% pi
\def\pival{3.14159}
\begin{document}
\begin{tikzpicture}
\draw(0,0)--(2*\pival/3,2*\pival/\sqrtTh)--(4*\pival/3,0)--(2*\pival/3,-2*\pival/\sqrtTh)--cycle;
\fill[color=gray0](0,0)--(2*\pival/3,2*\pival/\sqrtTh)--(4*\pival/3,0)--(2*\pival/3,-2*\pival/\sqrtTh)--cycle;
\fill[color=gray1](2*\pival/3, 2*\pival/3/\sqrtTh)circle(1);
\fill[color=gray1](2*\pival/3,-2*\pival/3/\sqrtTh)circle(1);
\fill[color=gray2](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.5);
\fill[color=gray2](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.5);
\fill[color=gray3](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.25);
\fill[color=gray3](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.25);
\fill[color=gray4](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.125);
\fill[color=gray4](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.125);
\fill[color=gray5](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.0626);
\fill[color=gray5](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.0625);
\fill[color=gray6](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.03125);
\fill[color=gray6](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.03125);
\fill[color=gray7](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.015625);
\fill[color=gray7](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.015625);
\end{tikzpicture}
\end{document}

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figs/cell-coarse.fig/Makefile Normal file
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@ -0,0 +1,23 @@
PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex)))
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
all: $(PDFS)
$(PDFS):
pdflatex -jobname $(basename $@) $(patsubst %.pdf, %.tikz.tex, $@)
install: $(PROJECTNAME)
cp $^.pdf $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
rm -f $(addsuffix .out, $(PROJECTNAME))
clean-tex:
rm -f $(PDFS) $(SYNCTEXS)
clean: clean-aux clean-tex

28
figs/cell-coarse.fig/cell-coarse.tikz.tex Normal file
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\documentclass{standalone}
\usepackage{tikz}
\usepackage{graphene}
% rescale cells by
\def\rr{4}
\begin{document}
\begin{tikzpicture}
%\graphene{(0,0)}{12}{12}
\graphene{(-3,3*\sqrtTh)}{17}{16}
\foreach \i in {0,...,3}{
\draw[line width=1pt, color=blue](-1*\rr,-\i*\sqrtTh*\rr)--++(1.5*2*\i*\rr+3*\rr,\sqrtThOT*2*\i*\rr+\sqrtTh*\rr);
}
\foreach \i in {0,...,3}{
\draw[line width=1pt, color=blue](0.5*\rr+3*\i*\rr,-3.5*\sqrtTh*\rr)--++(-1.5*2*\i*\rr+12*\rr,-\sqrtThOT*2*\i*\rr+4*\sqrtTh*\rr);
}
\foreach \i in {0,...,3}{
\draw[line width=1pt, color=blue](-1*\rr,-\i*\sqrtTh*\rr)--++(-1.5*2*\i*\rr+10.5*\rr,+\sqrtThOT*2*\i*\rr-3.5*\sqrtTh*\rr);
}
\foreach \i in {0,...,3}{
\draw[line width=1pt, color=blue](-1*\rr+3*\i*\rr,\sqrtTh*\rr)--++(-1.5*2*\i*\rr+13.5*\rr,\sqrtThOT*2*\i*\rr-4.5*\sqrtTh*\rr);
}
\end{tikzpicture}
\end{document}

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figs/cell-coarse.fig/graphene.sty Symbolic link
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../lib/graphene.sty

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figs/cell.fig/Makefile Normal file
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PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex)))
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
all: $(PDFS)
$(PDFS):
pdflatex -jobname $(basename $@) $(patsubst %.pdf, %.tikz.tex, $@)
install: $(PROJECTNAME)
cp $^.pdf $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
rm -f $(addsuffix .out, $(PROJECTNAME))
clean-tex:
rm -f $(PDFS) $(SYNCTEXS)
clean: clean-aux clean-tex

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figs/cell.fig/cell.tikz.tex Normal file
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\documentclass{standalone}
\usepackage{tikz}
\usepackage{graphene}
\begin{document}
\begin{tikzpicture}
\graphene{(0,0)}{3}{3}
\foreach \i in {0,...,3}{
\draw[color=blue](-1,-\i*\sqrtTh)--++(1.5*2*\i+3,\sqrtThOT*2*\i+\sqrtTh);
}
\foreach \i in {0,...,3}{
\draw[color=blue](0.5+3*\i,-3.5*\sqrtTh)--++(-1.5*2*\i+12,-\sqrtThOT*2*\i+4*\sqrtTh);
}
\foreach \i in {0,...,3}{
\draw[color=blue](-1,-\i*\sqrtTh)--++(-1.5*2*\i+10.5,+\sqrtThOT*2*\i-3.5*\sqrtTh);
}
\foreach \i in {0,...,3}{
\draw[color=blue](-1+3*\i,\sqrtTh)--++(-1.5*2*\i+13.5,\sqrtThOT*2*\i-4.5*\sqrtTh);
}
\draw[color=red] (6,-\sqrtTh)++(0.5,.6)node[rotate=30]{$l_1$};
\draw[color=red](6,-\sqrtTh)++(0.5,-.6)node[rotate=-30]{$l_2$};
\pgfsetarrowsend{latex};
\draw[color=red,line width=1.5pt](6,-\sqrtTh)--++\Lo;
\draw[color=red,line width=1.5pt](6,-\sqrtTh)--++\Lt;
\end{tikzpicture}
\end{document}

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figs/cell.fig/graphene.sty Symbolic link
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../lib/graphene.sty

23
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PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex)))
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
all: $(PDFS)
$(PDFS):
pdflatex -jobname $(basename $@) $(patsubst %.pdf, %.tikz.tex, $@)
install: $(PROJECTNAME)
cp $^.pdf $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
rm -f $(addsuffix .out, $(PROJECTNAME))
clean-tex:
rm -f $(PDFS) $(SYNCTEXS)
clean: clean-aux clean-tex

1
figs/graphene.fig/graphene.sty Symbolic link
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../lib/graphene.sty

12
figs/graphene.fig/graphene.tikz.tex Normal file
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\documentclass{standalone}
\usepackage{tikz}
\usepackage{graphene}
\def\bsite#1{\fill#1circle(.1);}
\begin{document}
\begin{tikzpicture}
\graphene{(0,0)}{3}{3}
\end{tikzpicture}
\end{document}

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PROJECTNAME=graphene_vector_field
DATS=graphene_vector_field.dat
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
all: $(PDFS)
$(PDFS): $(DATS)
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
graphene_vector_field.dat:
meankondo -C graphene.mk > graphene-numkondo.mk
./gendat > $@
install: $(PDFS)
cp $^ $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
clean-dat:
rm -f $(DATS)
rm -f graphene-numkondo.mk
clean-tex:
rm -f $(PDFS)
clean: clean-aux clean-tex

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figs/hierarchical_graphene.fig/gendat Executable file
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#!/bin/bash
# location of numkondo config
config=$(dirname $0)/graphene-numkondo.mk
# range and number of points in each direction
minx=-2
maxx=2
nx=20
miny=-1
maxy=1
ny=20
# compute each point
for i in $(seq $nx); do
# alpha_0
alpha0=$(python -c "print($minx+($maxx-($minx))/($nx-1)*($i-1))")
for j in $(seq $ny); do
# alpha_1
alpha1=$(python -c "print($miny+($maxy-($miny))/($ny-1)*($j-1))")
# print alphas
echo -n "$alpha0 $alpha1 "
# compute step and select the relevant lines
dat=$(numkondo -N 1 -F -I "0:$alpha0,1:$alpha1" "$config" | sed -r '/^[^01]/d;s/^[0-9]*://;s/,//' | tr '\n' ' ')
echo "$dat"
done
done

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figs/hierarchical_graphene.fig/graphene.mk Normal file
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## This computes the logarithm of the flow equation
#!fields
# extrenal fields: xy0 where x=alpha, y=sigma
x:110,120,210,220
# internal fields: xy1 where x=alpha, y=sigma
i:111,121,211,221
# all are Fermions
f:110,120,210,220,111,121,211,221
&
#!groups
# different spins are independent
(111,211) (121,221)
&
#!preprocessor_variables
# psi's with internal fields
psiAU=(1/2)[f110]+[f111],
psiAD=(1/2)[f120]+[f121],
psiBU=(1/2)[f210]+[f211],
psiBD=(1/2)[f220]+[f221],
psiAU-=(1/2)[f-110]+[f-111],
psiAD-=(1/2)[f-120]+[f-121],
psiBU-=(1/2)[f-210]+[f-211],
psiBD-=(1/2)[f-220]+[f-221],
# operators with internal fields
O0=
<<$psiAU>*<$psiBU->>+
<<$psiBU>*<$psiAU->>+
<<$psiAD>*<$psiBD->>+
<<$psiBD>*<$psiAD->>,
O1=
<<$psiAU>*<$psiAU->*<$psiAD>*<$psiAD->>+
<<$psiBU>*<$psiBU->*<$psiBD>*<$psiBD->>,
O2=
<<$psiAU>*<$psiAD->*<$psiBD>*<$psiBU->>+
<<$psiBU>*<$psiBD->*<$psiAD>*<$psiAU->>+
<<$psiAD>*<$psiAU->*<$psiBU>*<$psiBD->>+
<<$psiBD>*<$psiBU->*<$psiAU>*<$psiAD->>,
O3=
<<$psiAU>*<$psiAU->*<$psiBU>*<$psiBU->>+
<<$psiAD>*<$psiAD->*<$psiBD>*<$psiBD->>,
O4=
<<$psiAU>*<$psiBU->*<$psiAD>*<$psiBD->>+
<<$psiBU>*<$psiAU->*<$psiBD>*<$psiAD->>,
O5=
<<$psiAU>*<$psiAU->*<$psiAD>*<$psiBU->*<$psiBU>*<$psiBD->>+
<<$psiAD>*<$psiAD->*<$psiAU>*<$psiBD->*<$psiBD>*<$psiBU->>+
<<$psiBU>*<$psiBU->*<$psiBD>*<$psiAU->*<$psiAU>*<$psiAD->>+
<<$psiBD>*<$psiBD->*<$psiBU>*<$psiAD->*<$psiAD>*<$psiAU->>,
O6=<<$psiAU>*<$psiAU->*<$psiAD>*<$psiAD->*<$psiBU>*<$psiBU->*<$psiBD>*<$psiBD->>,
# psi's without internal fields
phiAU=[f110],
phiAD=[f120],
phiBU=[f210],
phiBD=[f220],
phiAU-=[f-110],
phiAD-=[f-120],
phiBU-=[f-210],
phiBD-=[f-220],
# operators without internal fields
E0=
<<$phiAU>*<$phiBU->>+
<<$phiBU>*<$phiAU->>+
<<$phiAD>*<$phiBD->>+
<<$phiBD>*<$phiAD->>,
E1=
<<$phiAU>*<$phiAU->*<$phiAD>*<$phiAD->>+
<<$phiBU>*<$phiBU->*<$phiBD>*<$phiBD->>,
E2=
<<$phiAU>*<$phiAD->*<$phiBD>*<$phiBU->>+
<<$phiBU>*<$phiBD->*<$phiAD>*<$phiAU->>+
<<$phiAD>*<$phiAU->*<$phiBU>*<$phiBD->>+
<<$phiBD>*<$phiBU->*<$phiAU>*<$phiAD->>,
E3=
<<$phiAU>*<$phiAU->*<$phiBU>*<$phiBU->>+
<<$phiAD>*<$phiAD->*<$phiBD>*<$phiBD->>,
E4=
<<$phiAU>*<$phiBU->*<$phiAD>*<$phiBD->>+
<<$phiBU>*<$phiAU->*<$phiBD>*<$phiAD->>,
E5=
<<$phiAU>*<$phiAU->*<$phiAD>*<$phiBU->*<$phiBU>*<$phiBD->>+
<<$phiAD>*<$phiAD->*<$phiAU>*<$phiBD->*<$phiBD>*<$phiBU->>+
<<$phiBU>*<$phiBU->*<$phiBD>*<$phiAU->*<$phiAU>*<$phiAD->>+
<<$phiBD>*<$phiBD->*<$phiBU>*<$phiAD->*<$phiAD>*<$phiAU->>,
E6=<<$phiAU>*<$phiAU->*<$phiAD>*<$phiAD->*<$phiBU>*<$phiBU->*<$phiBD>*<$phiBD->>
&
#!propagator
111;211: 1 ,121;221: 1 ,
211;111: 1 ,221;121: 1
&
#!input_polynomial
<%exp<
<<[l0]>*<$O0>>+
<<[l1]>*<$O1>>+
<<[l2]>*<$O2>>+
<<[l3]>*<$O3>>+
<<[l4]>*<$O4>>+
<<[l5]>*<$O5>>+
<<[l6]>*<$O6>>
>>
&
#!postprocess_flow_equation
<<8>*<%log_1<$FLOW>>>
&
#!id_table
0: <$E0>,
1: <$E1>,
2: <$E2>,
3: <$E3>,
4: <$E4>,
5: <$E5>,
6: <$E6>
&
#!labels
0:"O0" ,
1:"O1" ,
2:"O2" ,
3:"O3" ,
4:"O4" ,
5:"O5" ,
6:"O6"

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figs/hierarchical_graphene.fig/graphene_vector_field.gnuplot Normal file
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set ylabel "$\\alpha_1$" norotate
set xlabel "$\\alpha_0$"
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 8,6 standalone
unset key
set pointsize 1
# color functions
rgb(r,g,b) = 65536 * int(r) + 256 * int(g) + int(b)
color(x) = rgb(x*255, 0 , (1-x)*255)
# get min/max
set yrange [-1000:1000]
stats "graphene_vector_field.dat" u (log10(sqrt(($3-$1)**2+($4-$2)**2)))
set xrange [-2:2]
set yrange [-1:1]
rescale=15
plot "graphene_vector_field.dat" u 1:2:(($3-$1)/sqrt(($3-$1)**2+($4-$2)**2)/rescale):(($4-$2)/sqrt(($3-$1)**2+($4-$2)**2)/rescale):(color((log10(sqrt(($3-$1)**2+($4-$2)**2))-STATS_min)/(STATS_max-STATS_min))) with vec filled head linecolor rgb variable

32
figs/hierarchical_sd.fig/Makefile Normal file
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PROJECTNAME=sd_vector_field
DATS=sd_vector_field.dat
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
all: $(PDFS)
$(PDFS): $(DATS)
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
sd_vector_field.dat:
meankondo -C sd.mk > sd-numkondo.mk
./gendat > $@
install: $(PDFS)
cp $^ $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
clean-dat:
rm -f $(DATS)
rm -f sd-numkondo.mk
clean-tex:
rm -f $(PDFS)
clean: clean-aux clean-tex

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figs/hierarchical_sd.fig/gendat Executable file
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#!/bin/bash
# location of numkondo config
config=$(dirname $0)/sd-numkondo.mk
# range and number of points in each direction
minx=-1
maxx=0.5
nx=20
miny=-0.4
maxy=0.4
ny=20
# compute each point
for i in $(seq $nx); do
# alpha_0
alpha0=$(python -c "print($minx+($maxx-($minx))/($nx-1)*($i-1))")
for j in $(seq $ny); do
# alpha_1
alpha1=$(python -c "print($miny+($maxy-($miny))/($ny-1)*($j-1))")
# print alphas
echo -n "$alpha0 $alpha1 "
# compute step and select the relevant lines
dat=$(numkondo -N 1 -F -I "0:$alpha0,1:$alpha1" "$config" | sed -r '/^[^01]/d;s/^[0-9]*://;s/,//' | tr '\n' ' ')
echo "$dat"
done
done

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#!fields
x:100,110
i:101,102,111,112
h:400,410,420
f:100,110,101,102,111,112
a:400,410,420
&
#!preprocessor_variables
psiAu1=[f100]+[f101],
psiAu2=[f100]+[f102],
psiAd1=[f110]+[f111],
psiAd2=[f110]+[f112],
psiAu1-=[f-100]+[f-101],
psiAu2-=[f-100]+[f-102],
psiAd1-=[f-110]+[f-111],
psiAd2-=[f-110]+[f-112],
A11=<<$psiAu1>*<$psiAd1->>+<<$psiAd1>*<$psiAu1->>,
A12=<<$psiAu2>*<$psiAd2->>+<<$psiAd2>*<$psiAu2->>,
A21=<<(-1)s{-1}>*<$psiAu1>*<$psiAd1->>+<<s{-1}>*<$psiAd1>*<$psiAu1->>,
A22=<<(-1)s{-1}>*<$psiAu2>*<$psiAd2->>+<<s{-1}>*<$psiAd2>*<$psiAu2->>,
A31=<<$psiAu1>*<$psiAu1->>+<<-1>*<$psiAd1>*<$psiAd1->>,
A32=<<$psiAu2>*<$psiAu2->>+<<-1>*<$psiAd2>*<$psiAd2->>,
AB1=<<$A11>*<[f400]>>+<<$A21>*<[f410]>>+<<$A31>*<[f420]>>,
AA1=<<$A11>*<$A11>>+<<$A21>*<$A21>>+<<$A31>*<$A31>>,
AB2=<<$A12>*<[f400]>>+<<$A22>*<[f410]>>+<<$A32>*<[f420]>>,
AA2=<<$A12>*<$A12>>+<<$A22>*<$A22>>+<<$A32>*<$A32>>,
A1=[f100][f-110] + [f110][f-100],
A2=((-1)s{-1})[f100][f-110] + (s{-1})[f110][f-100],
A3=[f100][f-100] + (-1)[f110][f-110],
AB=<<$A1>*<[f400]>>+<<$A2>*<[f410]>>+<<$A3>*<[f420]>>,
AA=<<$A1>*<$A1>>+<<$A2>*<$A2>>+<<$A3>*<$A3>>
&
#!identities
[f400][f400]=(1),
[f400][f410]=(s{-1})[f420],
[f420][f410]=((-1)s{-1})[f400],
[f410][f410]=(1),
[f410][f420]=(s{-1})[f400],
[f400][f420]=((-1)s{-1})[f410],
[f420][f420]=(1),
[f420][f400]=(s{-1})[f410],
[f410][f400]=((-1)s{-1})[f420]
&
#!propagator
101;102: 1 ,111;112: 1 ,
102;101: -1 ,112;111: -1
&
#!input_polynomial
<
<1>
+ <<(1/2)[l0]>*<$AB1>>
+ <<(1/2)[l1]>*<$AA1>>
>*<
<1>
+ <<(1/2)[l0]>*<$AB2>>
+ <<(1/2)[l1]>*<$AA2>>
>
&
#!id_table
0: <$AB>,
1: <2>*<$AA>
&
#!labels
0:"at" ,
1:"aa" ,

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figs/hierarchical_sd.fig/sd_vector_field.gnuplot Normal file
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set ylabel "$\\ell_1$" norotate
set xlabel "$\\ell_0$"
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 8,6 standalone
unset key
set pointsize 1
# color functions
rgb(r,g,b) = 65536 * int(r) + 256 * int(g) + int(b)
color(x) = rgb(x*255, 0 , (1-x)*255)
# get min/max
set yrange [-1000:1000]
stats "sd_vector_field.dat" u (log10(sqrt(($3-$1)**2+($4-$2)**2)))
set xrange [-1:0.5]
set yrange [-0.4:0.4]
rescale=40
plot "sd_vector_field.dat" u 1:2:(($3-$1)/sqrt(($3-$1)**2+($4-$2)**2)/rescale):(($4-$2)/sqrt(($3-$1)**2+($4-$2)**2)/rescale):(color((log10(sqrt(($3-$1)**2+($4-$2)**2))-STATS_min)/(STATS_max-STATS_min))) with vec filled head linecolor rgb variable

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% sqrt(3)/2
\def\sqrtThOT{0.866}
% sqrt(3)
\def\sqrtTh{1.732}
% pi
\def\pival{3.14159}
% base vectorsj
\def\Lo{(1.5,\sqrtThOT)}
\def\Lt{(1.5,-\sqrtThOT)}
\def\mLo{(-1.5,-\sqrtThOT)}
\def\mLt{(-1.5,\sqrtThOT)}
% filled square at #1 of side-length #2
\def\fullsquare#1#2{\fill#1++(-#2,-#2)--++(#2,0)--++(#2,0)--++(0,#2)--++(0,#2)--++(-#2,0)--++(-#2,0)--++(0,-#2)--++(0,-#2);}
% in color
\def\fullsquarecolor#1#2#3{\fill[color=#3]#1++(-#2,-#2)--++(#2,0)--++(#2,0)--++(0,#2)--++(0,#2)--++(-#2,0)--++(-#2,0)--++(0,-#2)--++(0,-#2);}
% type-a site at #1
\def\asite#1{\fill#1circle(.1);}
% in color
\def\asitec#1#2{\fill[color=#2]#1circle(.1);}
% type-b site at #1
\def\bsite#1{\fullsquare{#1}{.1}}
% in color
\def\bsitec#1#2{\fullsquarecolor{#1}{.1}{#2}}
% base cell with a site at #1
\def\cell#1{
\draw#1--++(0:1);
\draw#1--++(120:1);
\draw#1--++(240:1);
\asite{#1}
\draw#1++(1,0)--++(0:-1);
\draw#1++(1,0)--++(120:-1);
\draw#1++(1,0)--++(240:-1);
\bsite{#1++(1,0)}
}
% grpahene grid at #1 of width #2 and height #3
\def\graphene#1#2#3{
\foreach \i in {0,...,#2}{
\foreach \j in {0,...,#3}{
\cell{#1++(\i*3,-2*\j*\sqrtThOT)}
\cell{#1++(\i*3+1.5,\sqrtThOT-2*\j*\sqrtThOT)}
}
}
}

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%%
%% Ian's class file
%%
%% TeX format
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
%% class name
\ProvidesClass{ian}[2017/09/29]
%% boolean to signal that this class is being used
\newif\ifianclass
\ianclasstrue
%% options
% no section numbering in equations
\DeclareOption{section_in_eq}{\sectionsineqtrue}
\DeclareOption{section_in_fig}{\sectionsinfigtrue}
\DeclareOption{section_in_all}{\sectionsineqtrue\sectionsinfigtrue}
\DeclareOption{subsection_in_eq}{\subsectionsineqtrue}
\DeclareOption{subsection_in_fig}{\subsectionsinfigtrue}
\DeclareOption{subsection_in_all}{\subsectionsineqtrue\subsectionsinfigtrue}
\DeclareOption{no_section_in_eq}{\sectionsineqfalse}
\DeclareOption{no_section_in_fig}{\sectionsinfigfalse}
\DeclareOption{no_section_in_all}{\sectionsineqfalse\sectionsinfigfalse}
\DeclareOption{no_subsection_in_eq}{\subsectionsineqfalse}
\DeclareOption{no_subsection_in_fig}{\subsectionsinfigfalse}
\DeclareOption{no_subsection_in_all}{\subsectionsineqfalse\subsectionsinfigfalse}
\def\ian@defaultoptions{
\ExecuteOptions{section_in_all, no_subsection_in_all}
\ProcessOptions
%% required packages
\RequirePackage{color}
\RequirePackage{marginnote}
\RequirePackage{amssymb}
\PassOptionsToPackage{hidelinks}{hyperref}
\RequirePackage{hyperref}
\pagestyle{plain}
}
%% paper dimensions
\setlength\paperheight{297mm}
\setlength\paperwidth{210mm}
%% fonts
\input{size11.clo}
\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
%% text dimensions
\hoffset=-50pt
\voffset=-72pt
\textwidth=460pt
\textheight=704pt
%% remove default indentation
\parindent=0pt
%% indent command
\def\indent{\hskip20pt}
%% something is wrong with \thepage, redefine it
\gdef\thepage{\the\c@page}
%% array lines (to use the array environment)
\setlength\arraycolsep{5\p@}
\setlength\arrayrulewidth{.4\p@}
%% correct vertical alignment at the end of a document
\AtEndDocument{
\vfill
\eject
}
%% hyperlinks
% hyperlinkcounter
\newcounter{lncount}
% hyperref anchor
\def\hrefanchor{%
\stepcounter{lncount}%
\hypertarget{ln.\thelncount}{}%
}
%% define a command and write it to aux file
\def\outdef#1#2{%
% define command%
\expandafter\xdef\csname #1\endcsname{#2}%
% hyperlink number%
\expandafter\xdef\csname #1@hl\endcsname{\thelncount}%
% write command to aux%
\immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1\endcsname{\csname #1\endcsname}}%
\immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1@hl\endcsname{\thelncount}}%
}
%% can call commands even when they are not defined
\def\safe#1{%
\ifdefined#1%
#1%
\else%
{\color{red}\bf?}%
\fi%
}
%% define a label for the latest tag
%% label defines a command containing the string stored in \tag
\def\deflabel{
\def\label##1{\expandafter\outdef{label@##1}{\safe\tag}}
\def\ref##1{%
% check whether the label is defined (hyperlink runs into errors if this check is omitted)
\ifcsname label@##1@hl\endcsname%
\hyperlink{ln.\csname label@##1@hl\endcsname}{{\color{blue}\safe\csname label@##1\endcsname}}%
\else%
\ifcsname label@##1\endcsname%
{\color{blue}\csname ##1\endcsname}%
\else%
{\bf ??}%
\fi%
\fi%
}
}
%% make a custom link at any given location in the document
\def\makelink#1#2{%
\hrefanchor%
\outdef{label@#1}{#2}%
}
%% section command
% counter
\newcounter{sectioncount}
% space before section
\newlength\secskip
\setlength\secskip{40pt}
% a prefix to put before the section number, e.g. A for appendices
\def\sectionprefix{}
% define some lengths
\newlength\secnumwidth
\newlength\sectitlewidth
\def\section#1{
% reset counters
\stepcounter{sectioncount}
\setcounter{subsectioncount}{0}
\ifsectionsineq
\setcounter{seqcount}0
\fi
\ifsectionsinfig
\setcounter{figcount}0
\fi
% space before section (if not first)
\ifnum\thesectioncount>1
\vskip\secskip
\penalty-1000
\fi
% hyperref anchor
\hrefanchor
% define tag (for \label)
\xdef\tag{\sectionprefix\thesectioncount}
% get widths
\def\@secnum{{\bf\Large\sectionprefix\thesectioncount.\hskip10pt}}
\settowidth\secnumwidth{\@secnum}
\setlength\sectitlewidth\textwidth
\addtolength\sectitlewidth{-\secnumwidth}
% print name
\parbox{\textwidth}{
\@secnum
\parbox[t]{\sectitlewidth}{\Large\bf #1}}
% write to table of contents
\iftoc
% save lncount in aux variable which is written to toc
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@sec.\thesectioncount\endcsname{\thelncount}}
\write\tocoutput{\noexpand\tocsection{#1}{\thepage}}
\fi
%space
\par\penalty10000
\bigskip\penalty10000
}
%% subsection
% counter
\newcounter{subsectioncount}
% space before subsection
\newlength\subsecskip
\setlength\subsecskip{30pt}
\def\subsection#1{
% counters
\stepcounter{subsectioncount}
\setcounter{subsubsectioncount}{0}
\ifsubsectionsineq
\setcounter{seqcount}0
\fi
\ifsubsectionsinfig
\setcounter{figcount}0
\fi
% space before subsection (if not first)
\ifnum\thesubsectioncount>1
\vskip\subsecskip
\penalty-500
\fi
% hyperref anchor
\hrefanchor
% define tag (for \label)
\xdef\tag{\sectionprefix\thesectioncount.\thesubsectioncount}
% get widths
\def\@secnum{{\bf\large\hskip.5cm\sectionprefix\thesectioncount.\thesubsectioncount.\hskip5pt}}
\settowidth\secnumwidth{\@secnum}
\setlength\sectitlewidth\textwidth
\addtolength\sectitlewidth{-\secnumwidth}
% print name
\parbox{\textwidth}{
\@secnum
\parbox[t]{\sectitlewidth}{\large\bf #1}}
% write to table of contents
\iftoc
% save lncount in aux variable which is written to toc
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@subsec.\thesectioncount.\thesubsectioncount\endcsname{\thelncount}}
\write\tocoutput{\noexpand\tocsubsection{#1}{\thepage}}
\fi
% space
\par\penalty10000
\medskip\penalty10000
}
%% subsubsection
% counter
\newcounter{subsubsectioncount}
% space before subsubsection
\newlength\subsubsecskip
\setlength\subsubsecskip{20pt}
\def\subsubsection#1{
% counters
\stepcounter{subsubsectioncount}
% space before subsubsection (if not first)
\ifnum\thesubsubsectioncount>1
\vskip\subsubsecskip
\penalty-500
\fi
% hyperref anchor
\hrefanchor
% define tag (for \label)
\xdef\tag{\sectionprefix\thesectioncount.\thesubsectioncount.\thesubsubsectioncount}
% get widths
</