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/segments.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/segments.tikz.tex')
-rw-r--r-- | figs/polymer_example.fig/segments.tikz.tex | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/figs/polymer_example.fig/segments.tikz.tex b/figs/polymer_example.fig/segments.tikz.tex index 9669e3b..b854f54 100644 --- a/figs/polymer_example.fig/segments.tikz.tex +++ b/figs/polymer_example.fig/segments.tikz.tex @@ -22,8 +22,8 @@ \fill[color=magenta](13,21.5)--++(18,0)--++(0.5,0.5)--++(0,7)--++(-0.5,0.5)--++(-18,0)--++(-0.5,-0.5)--++(0,-7)--cycle; \fill[color=white](14,23.5)--++(16,0)--++(0.5,0.5)--++(0,3)--++(-0.5,0.5)--++(-16,0)--++(-0.5,-0.5)--++(0,-3)--cycle; % cyan -\fill[color=cyan](23,11.5)--++(7,0)--++(0.5,0.5)--++(0,5)--++(-0.5,0.5)--++(-7,0)--++(-0.5,-0.5)--++(0,-5)--cycle; -\fill[color=white](24,13.5)--++(5,0)--++(0.5,0.5)--++(0,1)--++(-0.5,0.5)--++(-5,0)--++(-0.5,-0.5)--++(0,-1)--cycle; +\fill[color=cyan](25,11.5)--++(3,0)--++(0.5,0.5)--++(0,5)--++(-0.5,0.5)--++(-3,0)--++(-0.5,-0.5)--++(0,-5)--cycle; +\fill[color=white](26,13.5)--++(1,0)--++(0.5,0.5)--++(0,1)--++(-0.5,0.5)--++(-1,0)--++(-0.5,-0.5)--++(0,-1)--cycle; % orange \fill[color=orange](15,23.5)--++(5,0)--++(0.5,0.5)--++(0,3)--++(-0.5,0.5)--++(-5,0)--++(-0.5,-0.5)--++(0,-3)--cycle; \fill[color=white](17,24.5)--++(1,0)--++(0.5,0.5)--++(0,1)--++(-0.5,0.5)--++(-1,0)--++(-0.5,-0.5)--++(0,-1)--cycle; @@ -71,8 +71,8 @@ \draw[color=teal, line width=15pt](20.5,\i)--++(12,0); } \foreach \i in {12,...,17}{ - \draw[color=teal, line width=15pt](20.5,\i)--++(2,0); - \draw[color=teal, line width=15pt](30.5,\i)--++(2,0); + \draw[color=teal, line width=15pt](20.5,\i)--++(4,0); + \draw[color=teal, line width=15pt](28.5,\i)--++(4,0); } \foreach \i in {18,...,19}{ \draw[color=teal, line width=15pt](20.5,\i)--++(12,0); @@ -85,7 +85,7 @@ } \draw[color=teal, line width=15pt](10.5,30)--++(22,0); -\foreach \i in {24,...,29}{ +\foreach \i in {26,...,27}{ \draw[color=cyan, line width=15pt](\i,13.5)--++(0,2); } @@ -120,7 +120,7 @@ % magenta \draw[color=black, line width=5pt](13,21.5)--++(18,0)--++(0.5,0.5)--++(0,7)--++(-0.5,0.5)--++(-18,0)--++(-0.5,-0.5)--++(0,-7)--cycle; % cyan -\draw[color=black, line width=5pt](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=black, line width=5pt](25,11.5)--++(3,0)--++(0.5,0.5)--++(0,5)--++(-0.5,0.5)--++(-3,0)--++(-0.5,-0.5)--++(0,-5)--cycle; % orange \draw[color=black, line width=5pt](15,23.5)--++(5,0)--++(0.5,0.5)--++(0,3)--++(-0.5,0.5)--++(-5,0)--++(-0.5,-0.5)--++(0,-3)--cycle; %green |