As presentedat MCQM2018, on 2018-02-23HEADv1.0master

14 files changed, 1028 insertions, 0 deletions

diff --git a/Jauslin_MCQM_2018.tex b/Jauslin_MCQM_2018.tex
new file mode 100644
index 0000000..7609b39
--- /dev/null
+++ b/Jauslin_MCQM_2018.tex
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+\documentclass{ian-presentation}
+
+\usepackage[hidelinks]{hyperref}
+\usepackage{graphicx}
+\usepackage{dsfont}
+
+\begin{document}
+\pagestyle{empty}
+\hbox{}\vfil
+\bf\Large
+\hfil Liquid crystals\par
+\smallskip
+\hfil and the Heilmann-Lieb model\par
+\vfil
+\large
+\hfil Ian Jauslin
+\normalsize
+\vfil
+\hfil\rm joint with {\bf Elliott H. Lieb}\par
+\vfil
+arXiv: {\tt \href{http://arxiv.org/abs/1709.05297}{1709.05297}}
+\hfill{\tt \href{http://ian.jauslin.org}{http://ian.jauslin.org}}
+\eject
+
+\setcounter{page}1
+\pagestyle{plain}
+
+\title{Liquid crystals}
+\begin{itemize}
+  \item Orientational order and positional disorder.
+\end{itemize}
+\hfil\includegraphics[width=5cm]{nematic.png}
+\hfil\includegraphics[width=5cm]{chiral.png}
+\vfill
+\eject
+
+\title{History}
+\begin{itemize}
+  \item \href{http://dx.doi.org/10.1111/j.1749-6632.1949.tb27296.x}{[Onsager, 1949]}: mean field model for hard needles in $\mathbb R^3$.
+  \item \href{http://dx.doi.org/10.1007/BF01009518}{[Heilmann, Lieb, 1979]}: interacting dimers.
+\vphantom{
+  \item \href{http://dx.doi.org/10.1007/BF00535264}{[Bricmont, Kuroda, Lebowitz, 1984]}: hard needles in $\mathbb R^2$ with a {\it finite} number of orientations.
+  \item \href{http://dx.doi.org/10.1007/s10955-005-8085-8}{[Ioffe, Velenik, Zahradn\'\i k, 2006]}: hard rods in $\mathbb Z^2$ (variable length).
+  \item \href{http://dx.doi.org/10.1007/s00220-013-1767-1}{[Disertori, Giuliani, 2013]}: hard rods in $\mathbb Z^2$.
+}
+\end{itemize}
+\vfill
+\eject
+
+\title{Heilmann-Lieb model}
+\hfil\href{http://dx.doi.org/10.1007/BF01009518}{[Heilmann, Lieb, 1979]}
+\vfil
+\hfil\includegraphics[width=5cm]{grid.pdf}
+\vfil\eject
+
+\addtocounter{page}{-1}
+\title{Heilmann-Lieb model}
+\hfil\href{http://dx.doi.org/10.1007/BF01009518}{[Heilmann, Lieb, 1979]}
+\vfil
+\hfil\includegraphics[width=5cm]{dimers.pdf}
+\vfil\eject
+
+\addtocounter{page}{-1}
+\title{Heilmann-Lieb model}
+\hfil\href{http://dx.doi.org/10.1007/BF01009518}{[Heilmann, Lieb, 1979]}
+\vfil
+\hfil\includegraphics[width=5cm]{interaction.pdf}
+\vfil\eject
+
+\title{History}
+\begin{itemize}
+  \item \href{http://dx.doi.org/10.1111/j.1749-6632.1949.tb27296.x}{[Onsager, 1949]}: mean field model for hard needles in $\mathbb R^3$.
+  \item \href{http://dx.doi.org/10.1007/BF01009518}{[Heilmann, Lieb, 1979]}: interacting dimers.
+  \item \href{http://dx.doi.org/10.1007/BF00535264}{[Bricmont, Kuroda, Lebowitz, 1984]}: hard needles in $\mathbb R^2$.
+  \item \href{http://dx.doi.org/10.1007/s10955-005-8085-8}{[Ioffe, Velenik, Zahradn\'\i k, 2006]}: hard rods in $\mathbb Z^2$ (variable length).
+  \item \href{http://dx.doi.org/10.1007/s00220-013-1767-1}{[Disertori, Giuliani, 2013]}: hard rods in $\mathbb Z^2$.
+\end{itemize}
+\vfill
+\eject
+
+\title{Heilmann-Lieb conjecture}
+\vfill
+\begin{itemize}
+  \item \href{http://dx.doi.org/10.1007/s10955-015-1421-8}{[Alberici, 2016]}: different fugacities for horizontal and vertical dimers.
+  \vfill
+  \item \href{http://dx.doi.org/10.1103/PhysRevB.89.035128}{[Papanikolaou, Charrier, Fradkin, 2014]}: numerics.
+\end{itemize}
+\vfill
+\eject
+
+\title{Heilmann-Lieb model}
+\begin{itemize}
+  \item Grand-canonical Gibbs measure:
+  $$
+    \left<A\right>_{\mathrm v}
+    :=
+    \lim_{\Lambda\to\mathbb Z^2}
+    \frac1{\Xi_{\Lambda,\mathrm v}(z)}
+    \sum_{\underline\delta\in\Omega_{\mathrm v}(\Lambda)}A(\underline\delta)z^{|\underline\delta|}\prod_{\delta\neq \delta'\in \underline\delta}e^{\frac12J\mathds 1_{\delta\sim\delta'}}
+  $$
+  \vskip-15pt
+  \begin{itemize}
+    \item $\Lambda$: finite box.
+    \item $\Omega_{\mathrm v}(\Lambda)$: non-overlapping dimer configurations satisfying the boundary condition.
+    \item $z\geqslant 0$: fugacity.
+    \item $J\geqslant 0$: interaction strength.
+    \item $\mathds 1_{\delta\sim\delta'}$ indicator that dimers are adjacent and aligned.
+  \end{itemize}
+\end{itemize}
+\vfill
+\eject
+
+\title{Theorem}
+For $1\ll z\ll J$, $\|(x,y)\|_{\mathrm{HL}}:=J|x|+e^{-\frac32J}z^{-\frac12}|y|$,
+\begin{itemize}
+  \item Given two vertical edges $e_{\mathrm v},f_{\mathrm v}$, $\left<\mathds 1_{e_{\mathrm v}}\right>_{\mathrm v}$ is {\it independent} of $e_{\mathrm v}$ and
+  $$
+    \begin{array}{c}
+      \left<\mathds 1_{e_{\mathrm v}}\right>_{\mathrm v}=\frac12(1+O(e^{-\frac12J}z^{-\frac12}))
+      \\[0.3cm]
+      \left<\mathds 1_{e_{\mathrm v}}\mathds 1_{f_{\mathrm v}}\right>_{\mathrm v}
+      -\left<\mathds 1_{e_{\mathrm v}}\right>_{\mathrm v}
+      \left<\mathds 1_{f_{\mathrm v}}\right>_{\mathrm v}
+      =O(e^{-c\ \mathrm{dist}_{\mathrm{HL}}(e_{\mathrm v},f_{\mathrm v})})
+    \end{array}
+  $$
+  \vskip-5pt
+  \item Given two horizontal edges $e_{\mathrm h},f_{\mathrm h}$, $\left<\mathds 1_{e_{\mathrm h}}\right>_{\mathrm v}$ is {\it independent} of $e_{\mathrm h}$ and
+  $$
+    \begin{array}{c}
+      \left<\mathds 1_{e_{\mathrm h}}\right>_{\mathrm v}=O(e^{-3J})
+      \\[0.3cm]
+      \left<\mathds 1_{e_{\mathrm h}}\mathds 1_{f_{\mathrm v}}\right>_{\mathrm v}
+      -\left<\mathds 1_{e_{\mathrm h}}\right>_{\mathrm v}
+      \left<\mathds 1_{f_{\mathrm h}}\right>_{\mathrm v}
+      =O(e^{-3J-c\ \mathrm{dist}_{\mathrm{HL}}(e_{\mathrm v},f_{\mathrm v})})
+    \end{array}
+  $$
+\end{itemize}
+\vfill
+\eject
+
+\title{1D system}
+\begin{itemize}
+  \item \href{http://dx.doi.org/10.1007/BF01009518}{[Heilmann, Lieb, 1979]}: mostly vertical dimers.
+  \item {\it Only} vertical dimers: integrable.
+  \item Given two vertical edges $e_{\mathrm v},f_{\mathrm v}$, $\left<\mathds 1_{e_{\mathrm v}}\right>_{\mathrm v}$ is {\it independent} of $e_{\mathrm v}$ and
+  $$
+    \begin{array}{c}
+      \left<\mathds 1_{e_{\mathrm v}}\right>_{\mathrm v}=\frac12(1+O(e^{-\frac12J}z^{-\frac12}))
+      \\[0.3cm]
+      \left<\mathds 1_{e_{\mathrm v}}\mathds 1_{f_{\mathrm v}}\right>_{\mathrm v}
+      -\left<\mathds 1_{e_{\mathrm v}}\right>_{\mathrm v}
+      \left<\mathds 1_{f_{\mathrm v}}\right>_{\mathrm v}
+      =O(e^{-c\ \mathrm{dist}_{\mathrm{1D}}(e_{\mathrm v},f_{\mathrm v})})
+    \end{array}
+  $$
+  with $\|(x,y)\|_{\mathrm{1D}}:=e^{-\frac32J}z^{-\frac12}|y|$.
+\end{itemize}
+\vfill
+\eject
+
+\title{Peierls argument}
+\vfill
+\hfil\includegraphics[width=5cm]{dimer_contour.pdf}
+\vfill
+
+\end{document}
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..3446836
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,50 @@
+PROJECTNAME=$(basename $(wildcard *.tex))
+LIBS=$(notdir $(wildcard libs/*))
+FIGS=$(notdir $(wildcard figs/*.fig))
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME))
+
+all: $(PROJECTNAME)
+
+$(PROJECTNAME): $(LIBS) $(FIGS)
+	pdflatex -file-line-error $@.tex
+	pdflatex -synctex=1 $@.tex
+
+$(SYNCTEXS): $(LIBS) $(FIGS)
+	pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@)
+
+
+$(LIBS):
+	ln -fs libs/$@ ./
+
+
+figs: $(FIGS)
+
+$(FIGS):
+	make -C figs/$@
+	for pdf in $$(find figs/$@/ -name '*.pdf'); do ln -fs "$$pdf" ./ ; done
+	for png in $$(find figs/$@/ -name '*.png'); do ln -fs "$$png" ./ ; done
+
+
+clean-aux: clean-figs-aux
+	rm -f $(addsuffix .aux, $(PROJECTNAME))
+	rm -f $(addsuffix .log, $(PROJECTNAME))
+	rm -f $(addsuffix .out, $(PROJECTNAME))
+
+clean-libs:
+	rm -f $(LIBS)
+
+clean-figs:
+	$(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean; )
+	rm -f $(notdir $(wildcard figs/*.fig/*.pdf))
+	rm -f $(notdir $(wildcard figs/*.fig/*.png))
+
+clean-figs-aux:
+	$(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean-aux; )
+
+
+clean-tex:
+	rm -f $(PDFS) $(SYNCTEXS)
+
+clean: clean-aux clean-tex clean-libs clean-figs
diff --git a/README b/README
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index 0000000..442ee60
--- /dev/null
+++ b/README
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+This directory contains the source files to typeset the presentation, and
+generate the figures. This can be accomplished by running
+  make
+
+This document uses a custom class file, located in the 'libs' directory, which
+defines a number of commands.
+
+
+* Dependencies:
+
+  pdflatex
+  TeXlive packages:
+    amsfonts
+    graphics
+    hyperref
+    latex
+    pgf
+    standalone
+  GNU make
+  python3
+  gnuplot
+
+* Files:
+
+  Jauslin_MCQM_2018.tex:
+    main LaTeX file
+
+  libs:
+    custom LaTeX class file
+
+  figs:
+    source code for the figures
+
+  figs/dimer_example.fig/dimer_conf.py:
+    this python script randomly generates a suitable dimer configuration for
+    the figures grid.pdf, dimers.pdf, interaction.pdf, and dimer_contour.pdf
+
+  figs/atoms.fig/*.py:
+    this python script randomly generates configurations of non-overlapping
+    ellipsoids for the figures nematic.png and chiral.png.
diff --git a/figs/atoms.fig/Makefile b/figs/atoms.fig/Makefile
new file mode 100644
index 0000000..45913bb
--- /dev/null
+++ b/figs/atoms.fig/Makefile
@@ -0,0 +1,15 @@
+PROJECTNAME=nematic chiral
+PNGS=$(addsuffix .png, $(PROJECTNAME))
+
+all: $(PNGS)
+
+$(PNGS):
+	cp $(patsubst %.png, %, $@)-base.gp $(patsubst %.png, %, $@).gp
+	python $(patsubst %.png, %, $@).py >> $(patsubst %.png, %, $@).gp
+	gnuplot $(patsubst %.png, %, $@).gp > $@
+
+clean-aux:
+	rm -f $(addsuffix .gp, $(PROJECTNAME))
+
+clean: clean-aux
+	rm -f $(PNGS)
diff --git a/figs/atoms.fig/chiral-base.gp b/figs/atoms.fig/chiral-base.gp
new file mode 100644
index 0000000..5960ce6
--- /dev/null
+++ b/figs/atoms.fig/chiral-base.gp
@@ -0,0 +1,22 @@
+set terminal pngcairo size 2048,2048
+
+set key off
+unset colorbox
+unset border
+unset xtics
+unset ytics
+unset ztics
+
+set parametric
+
+set view 80,10,1.5
+set view equal xyz
+
+set isosample 100
+
+set pm3d depthorder
+set pm3d lighting primary 0.50 specular 0.6
+
+set palette defined (0 "#339999", 1 "#339999")
+
+splot \
diff --git a/figs/atoms.fig/chiral.py b/figs/atoms.fig/chiral.py
new file mode 100644
index 0000000..eed6df8
--- /dev/null
+++ b/figs/atoms.fig/chiral.py
@@ -0,0 +1,102 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+import sys
+
+# size of space
+L=30
+# number of lines
+H=5
+# heigh of lines
+height=5
+# number of rods per line
+N=16
+# aspect ratio
+a=10
+# spread in theta angle
+spread_t=pi/60
+# in phi
+spread_p=pi/60
+# in height
+spread_h=1/120
+
+# check whether two rods overlap
+def check_overlap(rod1,rod2):
+    # relative placement
+    relative_pos=unrotate(subtract(rod2[0],rod1[0]), rod1[1])
+    if(abs(relative_pos[0])<2 and abs(relative_pos[1])<2 and abs(relative_pos[2])<2):
+        return(True)
+    # relative angle
+    relative_ang=cart_to_spherical(unrotate(spherical_to_cart(rod2[1]), rod1[1]))
+    # exclusion volume
+    # rotate other rod
+    relative_pos=unrotate(relative_pos, [0,relative_ang[1]])
+    #if(abs(relative_pos[1])<2 and abs(relative_pos[0])-2<abs(sin(relative_ang[0]))*a and abs(relative_pos[2])-a-2<abs(cos(relative_ang[0])*a)):
+    if(abs(relative_pos[1])<2 and abs(relative_pos[0])-2<abs(sin(relative_ang[0]))*a and abs(sin(relative_ang[0])*relative_pos[2]-cos(relative_ang[0])*relative_pos[0])-2<abs(sin(relative_ang[0])*a)):
+        return(True)
+    return(False)
+
+# def subtract vectors
+def subtract(x,y):
+    return([x[0]-y[0],x[1]-y[1],x[2]-y[2]])
+# rotate vector
+def unrotate(x,w):
+    ret=[x[0],x[1],x[2]]
+    # rotate phi
+    tmp=cos(w[1])*ret[0]+sin(w[1])*ret[1]
+    ret[1]=-sin(w[1])*ret[0]+cos(w[1])*ret[1]
+    ret[0]=tmp
+    # rotate theta
+    tmp=cos(w[0])*ret[0]-sin(w[0])*ret[2]
+    ret[2]=sin(w[0])*ret[0]+cos(w[0])*ret[2]
+    ret[0]=tmp
+    return(ret)
+
+# convert coordinates
+def spherical_to_cart(w):
+    return([cos(w[1])*sin(w[0]),sin(w[1])*sin(w[0]),cos(w[0])])
+def cart_to_spherical(x):
+    w=[0,0]
+    w[0]=acos(x[2])
+    if(sin(w[0]==0)):
+        return([w[0],0])
+    c=x[0]/sin(w[0])
+    s=x[1]/sin(w[0])
+    # to avoid truncation errors
+    if(abs(c)>1 and abs(c)<1.0001):
+        if(c>0):
+            return([w[0],0])
+        else:
+            return([w[0],pi])
+    if(s>=0):
+        return([w[0],acos(c)])
+    return([w[0],2*pi-acos(c)])
+
+# configuration
+config=[]
+# add rods
+for h in range(H):
+    config_h=[]
+    while len(config_h)<N:
+        # random position and angles
+        x=[random.uniform(0,L), random.uniform(0,L), random.gauss(h*height,spread_h)]
+        w=[abs(random.gauss(pi/2,spread_t)), random.gauss(pi/2*(1-h/(H-1)),spread_p)]
+        # chek it does not interfere with other rods
+        fine=True
+        for rod in config+config_h:
+            if(check_overlap(rod,[x,w])):
+                fine=False
+                break
+        if fine:
+            config_h.append([x,w])
+    config=config+config_h
+
+for i in range(len(config)):
+    rod=config[i]
+    print(str(rod[0][0])+"+("+str(cos(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(-sin(rod[1][1]))+")*sin(u)*sin(v)+("+str(cos(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+    print(str(rod[0][1])+"+("+str(sin(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][1]))+")*sin(u)*sin(v)+("+str(sin(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+    print(str(rod[0][2])+"+("+str(-sin(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][0])*a)+")*cos(v)", end="  ")
+    print("with pm3d", end="")
+    if i<len(config)-1:
+        print(", \\")
diff --git a/figs/atoms.fig/nematic-base.gp b/figs/atoms.fig/nematic-base.gp
new file mode 100644
index 0000000..4de0ee2
--- /dev/null
+++ b/figs/atoms.fig/nematic-base.gp
@@ -0,0 +1,21 @@
+set terminal pngcairo size 2048,2048
+
+set key off
+unset colorbox
+unset border
+unset xtics
+unset ytics
+unset ztics
+
+set parametric
+
+set view equal xyz
+
+set isosample 100
+
+set pm3d depthorder
+set pm3d lighting primary 0.50 specular 0.6
+
+set palette defined (0 "#339999", 1 "#339999")
+
+splot \
diff --git a/figs/atoms.fig/nematic.py b/figs/atoms.fig/nematic.py
new file mode 100644
index 0000000..5c779c0
--- /dev/null
+++ b/figs/atoms.fig/nematic.py
@@ -0,0 +1,90 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+
+# size of space
+L=30
+# number of rods
+N=75
+# aspect ratio
+a=10
+# spread in theta angle
+spread=pi/30
+
+# check whether two rods overlap
+def check_overlap(rod1,rod2):
+    # relative placement
+    relative_pos=unrotate(subtract(rod2[0],rod1[0]), rod1[1])
+    if(abs(relative_pos[0])<2 and abs(relative_pos[1])<2 and abs(relative_pos[2])<2):
+        return(True)
+    # relative angle
+    relative_ang=cart_to_spherical(unrotate(spherical_to_cart(rod2[1]), rod1[1]))
+    # exclusion volume
+    # rotate other rod
+    relative_pos=unrotate(relative_pos, [0,relative_ang[1]])
+    #if(abs(relative_pos[1])<2 and abs(relative_pos[0])-2<abs(sin(relative_ang[0]))*a and abs(relative_pos[2])-a-2<abs(cos(relative_ang[0])*a)):
+    if(abs(relative_pos[1])<2 and abs(relative_pos[0])-2<abs(sin(relative_ang[0]))*a and abs(sin(relative_ang[0])*relative_pos[2]-cos(relative_ang[0])*relative_pos[0])-2<abs(sin(relative_ang[0])*a)):
+        return(True)
+    return(False)
+
+# def subtract vectors
+def subtract(x,y):
+    return([x[0]-y[0],x[1]-y[1],x[2]-y[2]])
+# rotate vector
+def unrotate(x,w):
+    ret=[x[0],x[1],x[2]]
+    # rotate phi
+    tmp=cos(w[1])*ret[0]+sin(w[1])*ret[1]
+    ret[1]=-sin(w[1])*ret[0]+cos(w[1])*ret[1]
+    ret[0]=tmp
+    # rotate theta
+    tmp=cos(w[0])*ret[0]-sin(w[0])*ret[2]
+    ret[2]=sin(w[0])*ret[0]+cos(w[0])*ret[2]
+    ret[0]=tmp
+    return(ret)
+
+# convert coordinates
+def spherical_to_cart(w):
+    return([cos(w[1])*sin(w[0]),sin(w[1])*sin(w[0]),cos(w[0])])
+def cart_to_spherical(x):
+    w=[0,0]
+    w[0]=acos(x[2])
+    if(sin(w[0]==0)):
+        return([w[0],0])
+    c=x[0]/sin(w[0])
+    s=x[1]/sin(w[0])
+    # to avoid truncation errors
+    if(abs(c)>1 and abs(c)<1.0001):
+        if(c>0):
+            return([w[0],0])
+        else:
+            return([w[0],pi])
+    if(s>=0):
+        return([w[0],acos(c)])
+    return([w[0],2*pi-acos(c)])
+
+# configuration
+config=[]
+# add rods
+while len(config)<N:
+    # random position and angles
+    x=[random.uniform(0,L), random.uniform(0,L), random.uniform(0,L)]
+    w=[abs(random.gauss(0,spread)), random.uniform(0,2*pi)]
+    # chek it does not interfere with other rods
+    fine=True
+    for rod in config:
+        if(check_overlap(rod,[x,w])):
+            fine=False
+            break
+    if fine:
+        config.append([x,w])
+
+for i in range(len(config)):
+    rod=config[i]
+    print(str(rod[0][0])+"+("+str(cos(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(-sin(rod[1][1]))+")*sin(u)*sin(v)+("+str(cos(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+    print(str(rod[0][1])+"+("+str(sin(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][1]))+")*sin(u)*sin(v)+("+str(sin(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+    print(str(rod[0][2])+"+("+str(-sin(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][0])*a)+")*cos(v)", end="  ")
+    print("with pm3d", end="")
+    if i<len(config)-1:
+        print(", \\")
diff --git a/figs/dimer_example.fig/Makefile b/figs/dimer_example.fig/Makefile
new file mode 100644
index 0000000..9e5f7a3
--- /dev/null
+++ b/figs/dimer_example.fig/Makefile
@@ -0,0 +1,32 @@
+PROJECTNAME=grid dimers interaction dimer_contour
+LIBS=$(notdir $(wildcard libs/*))
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+SOURCES=$(addsuffix .tikz.tex, $(PROJECTNAME))
+
+all: $(PDFS)
+
+$(PDFS): $(SOURCES) $(LIBS)
+	echo $(LIBS)
+	pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
+
+$(SOURCES):
+	python3 dimer_conf.py
+
+$(LIBS):
+	ln -fs libs/$@ ./
+
+clean-libs:
+	rm -f $(LIBS)
+
+clean-aux:
+	rm -f $(addsuffix .aux, $(PROJECTNAME))
+	rm -f $(addsuffix .log, $(PROJECTNAME))
+
+clean-tex:
+	rm -f $(PDFS)
+
+clean-sources:
+	rm -f $(SOURCES)
+
+clean: clean-libs clean-aux clean-tex clean-sources
diff --git a/figs/dimer_example.fig/dimer_conf.py b/figs/dimer_example.fig/dimer_conf.py
new file mode 100644
index 0000000..e693f61
--- /dev/null
+++ b/figs/dimer_example.fig/dimer_conf.py
@@ -0,0 +1,242 @@
+#!/usr/bin/env python3
+
+import random
+from math import *
+
+# size of the grid
+L=24
+# boundary thickness (must be even)
+l0=4
+# activity and interaction
+z=3
+J=5
+
+
+# draw random dimers in a select area
+def fill_dimers(mask,direction):
+    if(direction=="h"):
+        d=[1,0]
+    else:
+        d=[0,1]
+
+    dimers=[]
+
+    # keep track of which sites are occupied
+    occupied=[]
+    for i in range(L):
+        occupied.append([])
+        for j in range(L):
+            occupied[i].append(0)
+
+    for i in range(10000):
+        # pick a random edge (indexed by its lower-left corner)
+        e=None
+        while(e==None or e[0]+d[0]>=L or e[1]+d[1]>=L or mask[e[0]][e[1]]==0 or mask[e[0]+d[0]][e[1]+d[1]]==0):
+            e=[random.randint(0,L-1),random.randint(0,L-1)]
+        # check whether a dimer can be added to the edge
+        if(occupied[e[0]][e[1]]==0 and occupied[e[0]+d[0]][e[1]+d[1]]==0):
+            # number of interactions
+            interactions=0
+            if(e[0]+2*d[0]<L and e[1]+2*d[1]<L and occupied[e[0]+2*d[0]][e[1]+2*d[1]]==1):
+                interactions=interactions+1
+            if(e[0]-d[0]>=0 and e[1]-d[1]>=0 and occupied[e[0]-d[0]][e[1]-d[1]]==1):
+                interactions=interactions+1
+            # probability of adding the dimer
+            p=1/(1+1/z*exp(-J*interactions))
+            if(p>random.random()):
+                # add dimer
+                dimers.append(e)
+                occupied[e[0]][e[1]]=1
+                occupied[e[0]+d[0]][e[1]+d[1]]=1
+
+    return(dimers)
+
+# find interactions
+def interactions(dimers,direction):
+    if(direction=="h"):
+        d=[1,0]
+    else:
+        d=[0,1]
+    
+    out=[]
+    for d1 in dimers:
+        for d2 in dimers:
+            if(d1[0]-d2[0]==2*d[0] and d1[1]-d2[1]==2*d[1]):
+                out.append([d2[0]+d[0],d2[1]+d[1]])
+    return(out)
+
+
+# draw dimers
+def draw_dimers(v_dimers,h_dimers,file_desc,color):
+    for d in v_dimers:
+        print("\\dimer{[color="+color+"]("+str(d[0])+","+str(d[1])+")}v", file=file_desc)
+    print("", file=file_desc)
+    for d in h_dimers:
+        print("\\dimer{[color="+color+"]("+str(d[0])+","+str(d[1])+")}h", file=file_desc)
+    print("", file=file_desc)
+
+# draw interactions
+def draw_interactions(v_interactions,h_interactions,file_desc):
+    for d in v_interactions:
+        print("\\interaction{("+str(d[0])+","+str(d[1])+")}v", file=file_desc)
+    print("", file=file_desc)
+    for d in h_interactions:
+        print("\\interaction{("+str(d[0])+","+str(d[1])+")}h", file=file_desc)
+    print("", file=file_desc)
+
+# draw loops
+def draw_loops(loops,file_desc,color):
+    for loop in loops:
+        print("\\draw[color="+color+", line width=3pt]",end="",file=file_desc)
+        for e in loop:
+            print("("+str(e[0])+","+str(e[1])+")--",end="",file=file_desc)
+        print("cycle;",file=file_desc)
+
+# init tikz file
+def init_tikz(filename):
+    file_desc=open(filename,"w")
+    print("\\documentclass{standalone}\n\n\\usepackage{tikz}\n\\usepackage{dimer}\n\\usetikzlibrary{decorations.pathmorphing}\n\n\\begin{document}\n\\begin{tikzpicture}\n\n", file=file_desc)
+    return(file_desc)
+
+# close tikz file
+def close_tikz(file_desc):
+    print("\\end{tikzpicture}\n\\end{document}", file=file_desc)
+    file_desc.close()
+
+
+mu=int(L/2)
+
+# loops
+loop1=[]
+for i in range(0,2*l0):
+    loop1.append([mu-l0+i,mu+4.5])
+for i in range(0,4):
+    loop1.append([mu+l0-1+0.5,mu+4-i])
+for i in range(0,l0):
+    loop1.append([mu+l0+i,mu+0.5])
+for i in range(0,6):
+    loop1.append([mu+2*l0-1+0.5,mu-i])
+for i in range(0,4*l0):
+    loop1.append([mu+2*l0-1-i,mu-5.5])
+for i in range(0,6):
+    loop1.append([mu-2*l0-0.5,mu-5+i])
+for i in range(0,l0):
+    loop1.append([mu-2*l0+i,mu+0.5])
+for i in range(0,4):
+    loop1.append([mu-l0-0.5,mu+1+i])
+# core of loop1
+core_loop1=[]
+for i in range(0,2*l0-4):
+    core_loop1.append([mu-l0+2+i,mu+3.5])
+for i in range(0,3):
+    core_loop1.append([mu+l0-3+0.5,mu+3-i])
+core_loop1.append([mu+l0-2,mu+0.5])
+core_loop1.append([mu+l0-1,mu+0.5])
+for i in range(0,l0-2):
+    core_loop1.append([mu+l0+i,mu-1+0.5])
+for i in range(0,4):
+    core_loop1.append([mu+2*l0-3+0.5,mu-1-i])
+for i in range(0,4*l0-4):
+    core_loop1.append([mu+2*l0-3-i,mu-4.5])
+for i in range(0,4):
+    core_loop1.append([mu-2*l0+2-0.5,mu-4+i])
+for i in range(0,l0-2):
+    core_loop1.append([mu-2*l0+2+i,mu-1+0.5])
+core_loop1.append([mu-l0,mu+0.5])
+core_loop1.append([mu-l0+1,mu+0.5])
+for i in range(0,3):
+    core_loop1.append([mu-l0+2-0.5,mu+1+i])
+
+loop2=[[mu-1,mu+2.5],[mu-0.5,mu+2],[mu-0.5,mu+1],[mu-1,mu+0.5],[mu-1.5,mu+1],[mu-1.5,mu+2]]
+loop3=[[mu-1,mu-1.5],[mu,mu-1.5],[mu+0.5,mu-2],[mu+0.5,mu-3],[mu,mu-3.5],[mu-1,mu-3.5],[mu-1.5,mu-3],[mu-1.5,mu-2]]
+
+
+loops=[loop1,loop2,loop3]
+
+
+# masks
+# init
+v_mask=[]
+h_mask=[]
+for i in range(L):
+    v_mask.append([])
+    h_mask.append([])
+    for j in range(L):
+        v_mask[i].append(1)
+        h_mask[i].append(0)
+# draw masks
+for i in range(mu-l0,mu+l0):
+    for j in range(mu+1,mu+5):
+        v_mask[i][j]=0
+for i in range(mu-2*l0,mu+2*l0):
+    for j in range(mu-5,mu+1):
+        v_mask[i][j]=0
+for i in range(mu-l0+2,mu+l0-2):
+    for j in range(mu+1,mu+4):
+        h_mask[i][j]=1
+for i in range(mu-l0,mu+l0):
+    h_mask[i][mu]=1
+for i in range(mu-2*l0+2,mu+2*l0-2):
+    for j in range(mu-4,mu):
+        h_mask[i][j]=1
+h_mask[mu-1][mu+1]=0
+h_mask[mu-1][mu+2]=0
+h_mask[mu-1][mu-3]=0
+h_mask[mu-1][mu-2]=0
+h_mask[mu][mu-3]=0
+h_mask[mu][mu-2]=0
+
+# random dimers in mask
+v_dimers=fill_dimers(v_mask,"v")
+h_dimers=fill_dimers(h_mask,"h")
+
+# mantle dimers
+h_mantle=[]
+for i in range(0,l0):
+    h_mantle.append([mu-l0+2*i,mu+4])
+for i in range(0,4):
+    h_mantle.append([mu+l0-2,mu+4-i])
+    h_mantle.append([mu-l0,mu+4-i])
+for i in range(0,int(l0/2)):
+    h_mantle.append([mu+l0+2*i,mu])
+    h_mantle.append([mu-l0-2-2*i,mu])
+for i in range(0,5):
+    h_mantle.append([mu+2*l0-2,mu-i])
+    h_mantle.append([mu-2*l0,mu-i])
+for i in range(0,2*l0):
+    h_mantle.append([mu-2*l0+2*i,mu-5])
+
+v_mantle=[]
+v_mantle.append([mu-1,mu+1])
+v_mantle.append([mu-1,mu-3])
+v_mantle.append([mu,mu-3])
+
+# interactions
+v_interactions=interactions(v_dimers+v_mantle,"v")
+h_interactions=interactions(h_dimers+h_mantle,"h")
+
+
+# files
+
+grid=init_tikz("grid.tikz.tex")
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=grid)
+close_tikz(grid)
+
+dimers=init_tikz("dimers.tikz.tex")
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=dimers)
+draw_dimers(v_dimers+v_mantle,h_dimers+h_mantle,dimers,"black")
+close_tikz(dimers)
+
+interaction=init_tikz("interaction.tikz.tex")
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=interaction)
+draw_interactions(v_interactions,h_interactions,interaction)
+draw_dimers(v_dimers+v_mantle,h_dimers+h_mantle,interaction,"black")
+close_tikz(interaction)
+
+contour=init_tikz("dimer_contour.tikz.tex")
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=contour)
+draw_loops([loop1,loop2,loop3],contour,"blue")
+draw_interactions(v_interactions,h_interactions,contour)
+draw_dimers(v_dimers,h_dimers,contour,"black")
+draw_dimers(v_mantle,h_mantle,contour,"black")
+close_tikz(contour)
diff --git a/figs/dimer_example.fig/libs/dimer.sty b/figs/dimer_example.fig/libs/dimer.sty
new file mode 120000
index 0000000..2d83c8a
--- /dev/null
+++ b/figs/dimer_example.fig/libs/dimer.sty
@@ -0,0 +1 @@
+../../libs/dimer.sty
\ No newline at end of file
diff --git a/figs/libs/Makefile b/figs/libs/Makefile
new file mode 100644
index 0000000..994463b
--- /dev/null
+++ b/figs/libs/Makefile
@@ -0,0 +1,25 @@
+PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex)))
+LIBS=$(notdir $(wildcard libs/*))
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+
+all: $(PDFS)
+
+$(PDFS): $(LIBS)
+	echo $(LIBS)
+	pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
+
+$(LIBS):
+	ln -fs libs/$@ ./
+
+clean-libs:
+	rm -f $(LIBS)
+
+clean-aux:
+	rm -f $(addsuffix .aux, $(PROJECTNAME))
+	rm -f $(addsuffix .log, $(PROJECTNAME))
+
+clean-tex:
+	rm -f $(PDFS)
+
+clean: clean-libs clean-aux clean-tex
diff --git a/figs/libs/dimer.sty b/figs/libs/dimer.sty
new file mode 100644
index 0000000..0f087ef
--- /dev/null
+++ b/figs/libs/dimer.sty
@@ -0,0 +1,33 @@
+% square lattice (width #1, height #2, origin #3)
+\def\grid#1#2#3{
+  \foreach\i in {0,...,#2}{
+    \draw#3++(0,\i)--++(#1,0);
+  }
+  \foreach\i in {0,...,#1}{
+    \draw#3++(\i,0)--++(0,#2);
+  }
+}
+
+% dimer (bottom-left vertex #1, vertical or horizontal #2)
+\def\dimer#1#2{
+  \if#2h
+    \draw[line width=5pt]#1--++(1,0);
+    \fill#1circle(7pt);
+    \fill#1++(1,0)circle(7pt);
+  \else
+    \draw[line width=5pt]#1--++(0,1);
+    \fill#1circle(7pt);
+    \fill#1++(0,1)circle(7pt);
+  \fi
+}
+
+% interactions (bottom-left vertex #1, vertical or horizontal #2)
+\def\interaction#1#2{
+  \if#2h
+    \draw[line width=5pt, color=white]#1--++(1,0);
+    \draw[line width=4pt, decorate, decoration={snake}, color=red]#1--++(1,0);
+  \else
+    \draw[line width=5pt, color=white]#1--++(0,1);
+    \draw[line width=4pt, decorate, decoration={snake}, color=red]#1--++(0,1);
+  \fi
+}
diff --git a/libs/ian-presentation.cls b/libs/ian-presentation.cls
new file mode 100644
index 0000000..635680f
--- /dev/null
+++ b/libs/ian-presentation.cls
@@ -0,0 +1,187 @@
+%%
+%% Ian's presentation class
+%%
+
+%% TeX format
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+
+%% class name
+\ProvidesClass{ian-presentation}[2017/09/29]
+
+\def\ian@defaultoptions{
+  \pagestyle{plain}
+  \RequirePackage{color}
+  \RequirePackage{amssymb}
+}
+
+%% paper dimensions
+\setlength\paperheight{243pt}
+\setlength\paperwidth{432pt}
+
+%% fonts
+\input{size11.clo}
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
+
+%% text dimensions
+\textheight=208pt
+\textwidth=367.2pt
+\hoffset=-1in
+\voffset=-1in
+\oddsidemargin=24pt
+\evensidemargin=24pt
+\topmargin=8pt
+\headheight=0pt
+\headsep=0pt
+\marginparsep=0pt
+\marginparwidth=0pt
+\footskip=16pt
+
+
+%% remove default skips
+\parindent=0pt
+\parskip=0pt
+\baselineskip=0pt
+
+%% something is wrong with \thepage, redefine it
+\gdef\thepage{\the\c@page}
+
+%% correct vertical alignment at the end of a document
+\AtEndDocument{
+  % save total slide count
+  \immediate\write\@auxout{\noexpand\gdef\noexpand\slidecount{\thepage}}
+  \vfill
+  \eject
+}
+
+
+%% footer
+\def\ps@plain{
+  \def\@oddhead{}
+  \def\@evenhead{\@oddhead}
+  \def\@oddfoot{\tiny\hfill\thepage/\safe\slidecount\hfill}
+  \def\@evenfoot{\@oddfoot}
+}
+\def\ps@empty{
+  \def\@oddhead{}
+  \def\@evenhead{\@oddhead}
+  \def\@oddfoot{}
+  \def\@evenfoot{\@oddfoot}
+}
+
+
+%% title of slide
+\def\title#1{
+  \hfil{\bf\large #1}\par
+  \hfil\vrule width0.75\textwidth height0.3pt\par
+  \vskip5pt
+}
+
+
+%% hyperlinks
+% hyperlinkcounter
+\newcounter{lncount}
+% hyperref anchor
+\def\hrefanchor{%
+\stepcounter{lncount}%
+\hypertarget{ln.\thelncount}{}%
+}
+
+%% define a command and write it to aux file
+\def\outdef#1#2{%
+  % define command%
+  \expandafter\xdef\csname #1\endcsname{#2}%
+  % hyperlink number%
+  \expandafter\xdef\csname #1@hl\endcsname{\thelncount}%
+  % write command to aux%
+  \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1\endcsname{\csname #1\endcsname}}%
+  \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1@hl\endcsname{\thelncount}}%
+}
+
+%% can call commands even when they are not defined
+\def\safe#1{%
+  \ifdefined#1%
+    #1%
+  \else%
+    {\color{red}\bf?}%
+  \fi%
+}
+
+
+%% itemize
+\newlength\itemizeskip
+% left margin for items
+\setlength\itemizeskip{20pt}
+\newlength\itemizeseparator
+% space between the item symbol and the text
+\setlength\itemizeseparator{5pt}
+% penalty preceding an itemize
+\def\itemizepenalty{0}
+% counter counting the itemize level
+\newcounter{itemizecount}
+
+% item symbol
+\def\itemizept#1{
+  \ifnum#1=1
+    \textbullet
+  \else
+    $\scriptstyle\blacktriangleright$
+  \fi
+}
+
+\newlength\current@itemizeskip
+\setlength\current@itemizeskip{0pt}
+\def\itemize{
+  \par\penalty\itemizepenalty\medskip\penalty\itemizepenalty
+  \addtocounter{itemizecount}{1}
+  \addtolength\current@itemizeskip{\itemizeskip}
+  \leftskip\current@itemizeskip
+}
+\def\enditemize{
+  \addtocounter{itemizecount}{-1}
+  \addtolength\current@itemizeskip{-\itemizeskip}
+  \par\leftskip\current@itemizeskip
+  \medskip
+}
+\newlength\itempt@total
+\def\item{
+  \settowidth\itempt@total{\itemizept\theitemizecount}
+  \addtolength\itempt@total{\itemizeseparator}
+  \par
+  \medskip
+  \hskip-\itempt@total\itemizept\theitemizecount\hskip\itemizeseparator
+}
+
+%% enumerate
+\newcounter{enumerate@count}
+\def\enumerate{
+  \setcounter{enumerate@count}0
+  \let\olditem\item
+  \let\olditemizept\itemizept
+  \def\item{
+    % counter
+    \stepcounter{enumerate@count}
+    % set header
+    \def\itemizept{\theenumerate@count.}
+    % hyperref anchor
+    \hrefanchor
+    % define tag (for \label)
+    \xdef\tag{\theenumerate@count}
+    \olditem
+  }
+  \itemize
+}
+\def\endenumerate{
+  \enditemize
+  \let\item\olditem
+  \let\itemizept\olditemizept
+}
+
+
+%% end
+\ian@defaultoptions
+
+\endinput