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.
658 lines
16 KiB
TeX
658 lines
16 KiB
TeX
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% save lncount in aux variable which is written to toc
|
|
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@references\endcsname{\thelncount}}
|
|
\write\tocoutput{\noexpand\tocreferences{\thepage}}\penalty10000
|
|
\fi
|
|
|
|
% write
|
|
{\bf \LARGE References}\par\penalty10000\bigskip\penalty10000
|
|
% width of header
|
|
\settowidth\bibheader{[#1]}
|
|
\leftskip\bibheader
|
|
}
|
|
% end environment
|
|
\def\endthebibliography{
|
|
\par\leftskip0pt
|
|
}
|
|
|
|
%% bibitem command
|
|
\def\bibitem[#1]#2{%
|
|
\hrefanchor%
|
|
\outdef{label@cite#2}{#1}%
|
|
\hskip-\bibheader%
|
|
\makebox[\bibheader]{\cite{#2}\hfill}%
|
|
}
|
|
|
|
%% cite command (adapted from latex.ltx)
|
|
% @tempswa is set to true when there is an optional argument
|
|
\newif\@tempswa
|
|
\def\cite{%
|
|
% check whether there is an optional argument (if there is none, add on empty '[]')
|
|
\@ifnextchar [{\@tempswatrue\@citex}{\@tempswafalse\@citex[]}%
|
|
}
|
|
% command with optional argument
|
|
\def\@citex[#1]#2{\leavevmode%
|
|
% initialize loop
|
|
\let\@citea\@empty%
|
|
% format
|
|
\@cite{%
|
|
% loop over ',' separated list
|
|
\@for\@citeb:=#2\do{%
|
|
% text to add at each iteration of the loop (separator between citations)
|
|
\@citea\def\@citea{,\ }%
|
|
% add entry to citelist
|
|
\@writecitation{\@citeb}%
|
|
\ref{cite\@citeb}%
|
|
}%
|
|
}%
|
|
% add optional argument text (as an argument to '\@cite')
|
|
{#1}%
|
|
}
|
|
\def\@cite#1#2{%
|
|
[#1\if@tempswa , #2\fi]%
|
|
}
|
|
%% add entry to citelist after checking it has not already been added
|
|
\def\@writecitation#1{%
|
|
\ifcsname if#1cited\endcsname%
|
|
\else%
|
|
\expandafter\newif\csname if#1cited\endcsname%
|
|
\immediate\write\@auxout{\string\citation{#1}}%
|
|
\fi%
|
|
}
|
|
|
|
%% table of contents
|
|
% boolean
|
|
\newif\iftoc
|
|
\def\tableofcontents{
|
|
{\bf \large Table of contents:}\par\penalty10000\bigskip\penalty10000
|
|
|
|
% copy content from file
|
|
\IfFileExists{\jobname.toc}{\input{\jobname.toc}}{{\tt error: table of contents missing}}
|
|
|
|
% open new toc
|
|
\newwrite\tocoutput
|
|
\immediate\openout\tocoutput=\jobname.toc
|
|
|
|
\toctrue
|
|
}
|
|
%% close file
|
|
\AtEndDocument{
|
|
% close toc
|
|
\iftoc
|
|
\immediate\closeout\tocoutput
|
|
\fi
|
|
}
|
|
|
|
|
|
%% fill line with dots
|
|
\def\leaderfill{\leaders\hbox to 1em {\hss. \hss}\hfill}
|
|
|
|
%% same as sectionprefix
|
|
\def\tocsectionprefix{}
|
|
|
|
%% toc formats
|
|
\newcounter{tocsectioncount}
|
|
\def\tocsection #1#2{
|
|
\stepcounter{tocsectioncount}
|
|
\setcounter{tocsubsectioncount}{0}
|
|
\setcounter{tocsubsubsectioncount}{0}
|
|
% write
|
|
\smallskip\hyperlink{ln.\csname toc@sec.\thetocsectioncount\endcsname}{{\bf \tocsectionprefix\thetocsectioncount}.\hskip5pt {\color{blue}#1}\leaderfill#2}\par
|
|
}
|
|
\newcounter{tocsubsectioncount}
|
|
\def\tocsubsection #1#2{
|
|
\stepcounter{tocsubsectioncount}
|
|
\setcounter{tocsubsubsectioncount}{0}
|
|
% write
|
|
{\hskip10pt\hyperlink{ln.\csname toc@subsec.\thetocsectioncount.\thetocsubsectioncount\endcsname}{{\bf \thetocsubsectioncount}.\hskip5pt {\color{blue}\small #1}\leaderfill#2}}\par
|
|
}
|
|
\newcounter{tocsubsubsectioncount}
|
|
\def\tocsubsubsection #1#2{
|
|
\stepcounter{tocsubsubsectioncount}
|
|
% write
|
|
{\hskip20pt\hyperlink{ln.\csname toc@subsubsec.\thetocsectioncount.\thetocsubsectioncount.\thetocsubsubsectioncount\endcsname}{{\bf \thetocsubsubsectioncount}.\hskip5pt {\color{blue}\small #1}\leaderfill#2}}\par
|
|
}
|
|
\def\tocappendices{
|
|
\medskip
|
|
\setcounter{tocsectioncount}0
|
|
{\bf Appendices}\par
|
|
\smallskip
|
|
\def\tocsectionprefix{A}
|
|
}
|
|
\def\tocreferences#1{
|
|
\medskip
|
|
{\hyperlink{ln.\csname toc@references\endcsname}{{\color{blue}\bf References}\leaderfill#1}}\par
|
|
\smallskip
|
|
}
|
|
|
|
|
|
%% definitions that must be loaded at begin document
|
|
\let\ian@olddocument\document
|
|
\def\document{
|
|
\ian@olddocument
|
|
|
|
\deflabel
|
|
\defcaption
|
|
}
|
|
|
|
%% end
|
|
\ian@defaultoptions
|
|
\endinput
|