84cec16dd8
Changed: Slight change in the statement of the main theorem: no long-range
positional order between any dimers, regardless of orientation.
Changed: Section 4 was completely reworked. It now consists of a
discussion, in which definitions and figures appear as needed.
The main lemma of the section was moved to the end.
Fixed: The definition of external contours had a serious typo in it.
Fixed: The definition of non-trivial polymers was backwards. What were
called non-trivial polymers are actually trivial, and vice versa.
Changed: The contour and polymer figures were changed to include an
example of a polymer with a non-trivial recursive structure.
Fixed: The clusters appearing in cluster expansions must be defined using
multisets instead of sets, as they were before. The notation was
adjusted accordingly.
Fixed: The expression of the Ursell function was missing a combinatorial
factor.
Fixed: When splitting a sum over clusters into a sum over a polymer and
the rest of the cluster, the sum over the multiplictity of the
polymer must be separated as well, in order to avoid overcounting.
Fixed: In the proof of lemma 5.2, the bound on \mathfrak x required a
better estimate on b_+ and nu_+.
Fixed: In the proof of lemma 5.2, the argument for why the number of bad
edges on the boundary of \iota is bounded by \ell_0(l-m) was wrong.
Added: In the proof of lemma 5.2, a figure was added to illustrate the
issue with bad edges.
Added: Some more minor points have been expanded to include more details.
Fixed: Miscellaneous typos and reformating.
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
color
doublestroke
graphics
hyperref
latex
marginnote
pgf
standalone
metafont
mfware
GNU make
python3
* Files:
Jauslin_Lieb_2017.tex:
main LaTeX file
libs:
custom LaTeX class and style files
figs:
source code for the figures
figs/dimer_example.fig/dimer_conf.py:
this python script randomly generates a suitable dimer configuration for
the figures interaction.pdf boundary.pdf bounding_loop.pdf and
dimer_contour.pdf
dimer_font:
metafont font with dimer symbols