diff options
author | Ian Jauslin <jauslin@ias.edu> | 2018-04-25 22:10:43 +0000 |
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committer | Ian Jauslin <jauslin@ias.edu> | 2018-04-26 05:27:22 +0000 |
commit | 84cec16dd8bbab11a43f00380a1e6354e3aa0c04 (patch) | |
tree | 3346280faa020c91cdebe9088082eaaf48165009 /figs/polymer_example.fig/mbbX.tikz.tex | |
parent | 52a5942994007acc29107f036c9b8f386b19399f (diff) |
Update to v0.1: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.
Diffstat (limited to 'figs/polymer_example.fig/mbbX.tikz.tex')
-rw-r--r-- | figs/polymer_example.fig/mbbX.tikz.tex | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/figs/polymer_example.fig/mbbX.tikz.tex b/figs/polymer_example.fig/mbbX.tikz.tex new file mode 100644 index 0000000..61db917 --- /dev/null +++ b/figs/polymer_example.fig/mbbX.tikz.tex @@ -0,0 +1,31 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{dimer} + +\begin{document} +\begin{tikzpicture} + +%% mantles +\fill[color=gray](2,1.5)--++(13,0)--++(0.5,0.5)--++(0,8)--++(-0.5,0.5)--++(-13,0)--++(-0.5,-0.5)--++(0,-8)--cycle; +\fill[color=white](4,2.5)--++(9,0)--++(0.5,0.5)--++(0,6)--++(-0.5,0.5)--++(-9,0)--++(-0.5,-0.5)--++(0,-6)--cycle; +\fill[color=gray](4,3.5)--++(4,0)--++(0.5,0.5)--++(0,4)--++(-0.5,0.5)--++(-4,0)--++(-0.5,-0.5)--++(0,-4)--cycle; +\fill[color=white](5,5.5)--++(2,0)--++(0.5,0.5)--++(0,0)--++(-0.5,0.5)--++(-2,0)--++(-0.5,-0.5)--++(0,-0)--cycle; + +%% segments +\foreach \i in {4,...,8}{ + \draw[color=gray, line width=15pt](8.5,\i)--++(5,0); +} + +%% grid +\grid{17}{12}{[color=lightgray](0,0)} + + +%% loops +\draw[color=black, line width=5pt](2,1.5)--++(13,0)--++(0.5,0.5)--++(0,8)--++(-0.5,0.5)--++(-13,0)--++(-0.5,-0.5)--++(0,-8)--cycle; +\draw[color=black, line width=5pt](3.5,4)--++(0.5,-0.5)--++(4,0)--++(0.5,0.5)--++(0,4)--++(-0.5,0.5)--++(-4,0)--++(-0.5,-0.5); +\draw[color=red, line width=10pt](3.5,8)--++(0,-4); + +\end{tikzpicture} +\end{document} + |