From 84cec16dd8bbab11a43f00380a1e6354e3aa0c04 Mon Sep 17 00:00:00 2001
From: Ian Jauslin <jauslin@ias.edu>
Date: Wed, 25 Apr 2018 22:10:43 +0000
Subject: 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.
---
 figs/polymer_example.fig/loops.tikz.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'figs/polymer_example.fig/loops.tikz.tex')

diff --git a/figs/polymer_example.fig/loops.tikz.tex b/figs/polymer_example.fig/loops.tikz.tex
index db06058..a25747f 100644
--- a/figs/polymer_example.fig/loops.tikz.tex
+++ b/figs/polymer_example.fig/loops.tikz.tex
@@ -20,7 +20,7 @@
 \draw[color=magenta, line width=1pt](13,21.5)--++(18,0)--++(0.5,0.5)--++(0,7)--++(-0.5,0.5)--++(-18,0)--++(-0.5,-0.5)--++(0,-7)--cycle;
 \draw[color=black](13,30.5)node{\it d};
 
-\draw[color=cyan, line width=1pt](23,11.5)--++(7,0)--++(0.5,0.5)--++(0,5)--++(-0.5,0.5)--++(-7,0)--++(-0.5,-0.5)--++(0,-5)--cycle;
+\draw[color=cyan, line width=1pt](25,11.5)--++(3,0)--++(0.5,0.5)--++(0,5)--++(-0.5,0.5)--++(-3,0)--++(-0.5,-0.5)--++(0,-5)--cycle;
 \draw[color=black](23,18.5)node{\it e};
 
 \draw[color=orange, line width=1pt](15,23.5)--++(5,0)--++(0.5,0.5)--++(0,3)--++(-0.5,0.5)--++(-5,0)--++(-0.5,-0.5)--++(0,-3)--cycle;
-- 
cgit v1.2.3-70-g09d2

