Update to v0.1:

Fixed: removed discussion on k-nearest neighbor exclusion models which do
not cover the lattice perfectly.

Fixed: extra assumption: particle configurations are determined by their
defects.

Fixed: miscellaneous minor tweaks, formatting and typos.

Added: discussion about Lee-Yang zeros and their relation to the
high-fugacity expansion.

Added: open problem: soft exclusion potentials.

Added: extended bibliography.

Changed: Particles in figures are now always centered on the lattice, not
the dual lattice.

Changed: improved Makefile.
This commit is contained in:
Ian Jauslin
2017-09-08 05:59:24 +00:00
parent 1b13e14750
commit c6fe9f4dfa
31 changed files with 155 additions and 94 deletions

View File

@ -5,9 +5,9 @@
\begin{document}
\begin{tikzpicture}
\foreach \i in {0,...,3}{
\foreach \j in {0,...,3}{
\cross{green}{(-2*\j,\j)++(\i,2*\i)}
\foreach \k in {0,...,3}{
\foreach \l in {0,...,3}{
\cross{cyan}{(-2*\l,\l)++(\k,2*\k)}
}
}
\end{tikzpicture}

View File

@ -5,9 +5,9 @@
\begin{document}
\begin{tikzpicture}
\foreach \i in {0,...,3}{
\foreach \j in {0,...,3}{
\cross{teal}{(-\j,2*\j)++(2*\i,\i)}
\foreach \k in {0,...,3}{
\foreach \l in {0,...,3}{
\cross{cyan}{(-\l,2*\l)++(2*\k,\k)}
}
}
\end{tikzpicture}

View File

@ -5,12 +5,12 @@
\begin{document}
\begin{tikzpicture}
\foreach\i in {2,...,4}{
\cross{cyan}{(2*\i,\i)}
\cross{cyan}{(5,15)++(\i,-2*\i)}
\foreach\k in {2,...,4}{
\cross{cyan}{(2*\k,\k)}
\cross{cyan}{(5,15)++(\k,-2*\k)}
}
\foreach\i in {1,...,3}{
\cross{cyan}{(-5,10)++(2*\i,\i)}
\foreach\k in {1,...,3}{
\cross{cyan}{(-5,10)++(2*\k,\k)}
}
\cross{cyan}{(3,5)}
\cross{cyan}{(5,9)}

View File

@ -5,6 +5,9 @@
\begin{document}
\begin{tikzpicture}
\ttsquare{black}{(2,1)}
\ttsquare{black}{(2,15)}
\foreach\i in {0,...,8}{
\ttsquare{teal}{(0,2*\i)}
\ttsquare{teal}{(4,2*\i)}
@ -15,10 +18,5 @@
\ttsquare{green}{(2,2*\i+1)}
}
\square{black}{(1.5,1.5)}
\square{black}{(2.5,1.5)}
\square{black}{(1.5,14.5)}
\square{black}{(2.5,14.5)}
\end{tikzpicture}
\end{document}

View File

@ -5,15 +5,15 @@
\begin{document}
\begin{tikzpicture}
\foreach\i in {0,...,5}{
\cross{teal}{(2*\i,\i)}
\cross{teal}{(-\i,2*\i)}
\cross{teal}{(-5,10)++(2*\i,\i)}
\cross{teal}{(5,15)++(\i,-2*\i)}
\foreach\k in {0,...,5}{
\cross{teal}{(2*\k,\k)}
\cross{teal}{(-\k,2*\k)}
\cross{teal}{(-5,10)++(2*\k,\k)}
\cross{teal}{(5,15)++(\k,-2*\k)}
}
\foreach\i in {0,...,2}{
\foreach\j in {0,...,1}{
\cross{green}{(3,5)++(\i,2*\i)++(-2*\j,\j)}
\foreach\k in {0,...,2}{
\foreach\l in {0,...,1}{
\cross{green}{(3,5)++(\k,2*\k)++(-2*\l,\l)}
}
}
\cross{green}{(-1,7)}

View File

@ -12,24 +12,38 @@
% cross (color #1, position #2)
\def\cross#1#2{
\fill[color=#1]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
\begin{scope}
\clip#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
\grid44{[color=white]#2++(-2,-2)}
\end{scope}
\draw[color=black]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
}
% 1x1 square (color #1, position #2)
\def\square#1#2{
\fill[color=#1]#2++(-0.5,-0.5)--++(0,1)--++(1,0)--++(0,-1)--cycle;
\draw[color=black]#2++(-0.5,-0.5)--++(0,1)--++(1,0)--++(0,-1)--cycle;
\draw[color=white]#2++(-0.5,0)--++(1,0);
\draw[color=white]#2++(0,-0.5)--++(0,1);
}
% 2x2 square (color #1, position #2)
\def\ttsquare#1#2{
\fill[color=#1]#2++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle;
\draw[color=black]#2++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle;
\draw[color=white]#2++(-1,0)--++(2,0);
\draw[color=white]#2++(0,-1)--++(0,2);
}
\def\ttsquareempty#1{
\draw[color=black]#1++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle;
}
% diamond (color #1, position #2)
\def\diamond#1#2{
\fill[color=#1]#2++(0,-1)--++(1,1)--++(-1,1)--++(-1,-1)--cycle;
\begin{scope}
\clip#2++(0,-1)--++(1,1)--++(-1,1)--++(-1,-1)--cycle;
\grid22{[color=white]#2++(-1,-1)}
\end{scope}
\draw[color=black]#2++(0,-1)--++(1,1)--++(-1,1)--++(-1,-1)--cycle;
}

View File

@ -5,7 +5,7 @@
\begin{document}
\begin{tikzpicture}
\grid55{(-2.5,-2.5)}
\grid44{(-2,-2)}
\cross{cyan}{(0,0)}
\end{tikzpicture}
\end{document}