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Ian Jauslin, Elliott H. Lieb: Nematic liquid crystal phase in a system of interacting dimers and monomers, 2017 http://ian.jauslin.org/publications/17jlC
2 Commits 1 Branch 3 Tags 163 KiB
TeX 94.9%
Python 3.9%
Makefile 1.2%
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Ian Jauslin 84cec16dd8 Update to v0.1: 
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.
2018-04-26 05:27:22 +00:00
dimer_font Initial commit 2017-09-15 16:34:06 +00:00
figs Update to v0.1: 2018-04-26 05:27:22 +00:00
libs Update to v0.1: 2018-04-26 05:27:22 +00:00
Changelog Update to v0.1: 2018-04-26 05:27:22 +00:00
Jauslin_Lieb_2017.tex Update to v0.1: 2018-04-26 05:27:22 +00:00
Makefile Initial commit 2017-09-15 16:34:06 +00:00
README Initial commit 2017-09-15 16:34:06 +00:00

README 

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