As presented at Princeton University on 2018-04-04HEADv1.0master

25 files changed, 829 insertions, 0 deletions

diff --git a/figs/dimer_conf.fig/Makefile b/figs/dimer_conf.fig/Makefile
new file mode 100644
index 0000000..f4dcf58
--- /dev/null
+++ b/figs/dimer_conf.fig/Makefile
@@ -0,0 +1,32 @@
+PROJECTNAME=grid dimers interaction boundary 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_conf.fig/dimer_conf.py b/figs/dimer_conf.fig/dimer_conf.py
new file mode 100644
index 0000000..ec27036
--- /dev/null
+++ b/figs/dimer_conf.fig/dimer_conf.py
@@ -0,0 +1,251 @@
+#!/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)
+
+boundary=init_tikz("boundary.tikz.tex")
+print("\\fill[color=cyan](-0.5,-0.5)--++("+str(L)+",0)--++(0,"+str(l0)+")--++("+str(-L)+",0)--cycle;", file=boundary)
+print("\\fill[color=cyan](-0.5,"+str(L-l0-0.5)+")--++("+str(L)+",0)--++(0,"+str(l0)+")--++("+str(-L)+",0)--cycle;", file=boundary)
+print("", file=boundary)
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=boundary)
+draw_dimers(v_dimers+v_mantle,h_dimers+h_mantle,boundary,"black")
+close_tikz(boundary)
+
+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_conf.fig/libs/dimer.sty b/figs/dimer_conf.fig/libs/dimer.sty
new file mode 100644
index 0000000..0f087ef
--- /dev/null
+++ b/figs/dimer_conf.fig/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/figs/dimer_example.fig/Makefile b/figs/dimer_example.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/dimer_example.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile
\ No newline at end of file
diff --git a/figs/dimer_example.fig/cover.tikz.tex b/figs/dimer_example.fig/cover.tikz.tex
new file mode 100644
index 0000000..3f6b32c
--- /dev/null
+++ b/figs/dimer_example.fig/cover.tikz.tex
@@ -0,0 +1,20 @@
+\documentclass{standalone}
+\usepackage{tikz}
+\usepackage{dimer_example}
+
+\begin{document}
+\hfil\begin{tikzpicture}
+\basegraph
+
+\draw[line width=3pt](A2)--(A3);
+\draw[line width=3pt](A1)--(D4);
+\draw[line width=3pt](D3)--(D2);
+\draw[line width=3pt](A8)--(D1);
+\draw[line width=3pt](C1)--(A4);
+\draw[line width=3pt](A5)--(A6);
+\draw[line width=3pt](A7)--(B3);
+\draw[line width=3pt](B1)--(B2);
+
+\end{tikzpicture}
+
+\end{document}
diff --git a/figs/dimer_example.fig/graph.tikz.tex b/figs/dimer_example.fig/graph.tikz.tex
new file mode 100644
index 0000000..a628122
--- /dev/null
+++ b/figs/dimer_example.fig/graph.tikz.tex
@@ -0,0 +1,10 @@
+\documentclass{standalone}
+\usepackage{tikz}
+\usepackage{dimer_example}
+
+\begin{document}
+\hfil\begin{tikzpicture}
+\basegraph
+\end{tikzpicture}
+
+\end{document}
diff --git a/figs/dimer_example.fig/libs/dimer_example.sty b/figs/dimer_example.fig/libs/dimer_example.sty
new file mode 100644
index 0000000..46eb35b
--- /dev/null
+++ b/figs/dimer_example.fig/libs/dimer_example.sty
@@ -0,0 +1,66 @@
+\def\basegraph{
+  \path(0,0)++(-135:3)coordinate(A1);
+  \path(0,0)++( -90:3)coordinate(A2);
+  \path(0,0)++( -45:3)coordinate(A3);
+  \path(0,0)++(   0:3)coordinate(A4);
+  \path(0,0)++(  45:3)coordinate(A5);
+  \path(0,0)++(  90:3)coordinate(A6);
+  \path(0,0)++( 135:3)coordinate(A7);
+  \path(0,0)++( 180:3)coordinate(A8);
+
+  \path(0,0)++(-0.5,1)coordinate(B1);
+  \path(B1)++(1,0)coordinate(B2);
+  \path(B2)++(120:1)coordinate(B3);
+
+  \path(0,0)coordinate(C1);
+
+  \path(0,0)++(-0.5,-1)coordinate(D1);
+  \path(D1)--++(1,0)coordinate(D2);
+  \path(D2)--++(0,-1)coordinate(D3);
+  \path(D3)--++(-1,0)coordinate(D4);
+
+  \draw(A1)--(A2);
+  \draw(A2)--(A3);
+  \draw(A3)--(A4);
+  \draw(A4)--(A5);
+  \draw(A5)--(A6);
+  \draw(A6)--(A7);
+  \draw(A7)--(A8);
+  \draw(A8)--(A1);
+
+  \draw(B1)--(B2);
+  \draw(B2)--(B3);
+  \draw(B3)--(B1);
+
+  \draw(A8)--(C1);
+  \draw(C1)--(A4);
+
+  \draw(D1)--(D2);
+  \draw(D2)--(D3);
+  \draw(D4)--(D2);
+
+  \draw(A4)--(A6);
+  \draw(B1)--(A8);
+  \draw(B1)--(A7);
+  \draw(B3)--(A6);
+  \draw(B3)--(A7);
+  \draw(B2)--(A4);
+
+  \draw(D1)--(A8);
+  \draw(D1)--(A1);
+  \draw(D4)--(A1);
+  \draw(D3)--(A3);
+  \draw(D2)--(A4);
+
+
+  \foreach \i in {1,...,8}{
+    \fill(A\i)circle(0.1);
+  }
+  \fill(B1)circle(0.1);
+  \fill(B2)circle(0.1);
+  \fill(B3)circle(0.1);
+  \fill(C1)circle(0.1);
+  \foreach\i in {1,...,4}{
+    \fill(D\i)circle(0.1);
+  }
+}
diff --git a/figs/dimer_example.fig/mdcover.tikz.tex b/figs/dimer_example.fig/mdcover.tikz.tex
new file mode 100644
index 0000000..4752da8
--- /dev/null
+++ b/figs/dimer_example.fig/mdcover.tikz.tex
@@ -0,0 +1,18 @@
+\documentclass{standalone}
+\usepackage{tikz}
+\usepackage{dimer_example}
+
+\begin{document}
+\hfil\begin{tikzpicture}
+\basegraph
+
+\draw[line width=3pt](A2)--(A3);
+\draw[line width=3pt](A1)--(A8);
+\draw[line width=3pt](D4)--(D2);
+\draw[line width=3pt](C1)--(A4);
+\draw[line width=3pt](B3)--(A6);
+\draw[line width=3pt](A7)--(B1);
+
+\end{tikzpicture}
+
+\end{document}
diff --git a/figs/ising.fig/Makefile b/figs/ising.fig/Makefile
new file mode 100644
index 0000000..eeff491
--- /dev/null
+++ b/figs/ising.fig/Makefile
@@ -0,0 +1,38 @@
+PROJECTNAME=ising ising_blue ising_red transfer1 transfer2
+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 ising.py
+
+install: $(PDFS)
+	cp $^ $(INSTALLDIR)/
+
+install-sources: $(SOURCES)
+	cp $^ $(INSTALLDIR)/
+
+$(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/ising.fig/ising.py b/figs/ising.fig/ising.py
new file mode 100644
index 0000000..8dd1447
--- /dev/null
+++ b/figs/ising.fig/ising.py
@@ -0,0 +1,56 @@
+#!/usr/bin/env python3
+
+import random
+from math import *
+
+# size of the grid
+L=8
+
+# draw spins, probability of reds: p, only fill up to H
+def draw_spins(p, H, file_desc):
+    for i in range(L):
+        for j in range(H):
+            if(random.random()<p):
+                print("\\fill[color=red]("+str(i)+","+str(j)+")circle(0.2);", file=file_desc);
+            else:
+                print("\\fill[color=blue]("+str(i)+","+str(j)+")circle(0.2);", file=file_desc);
+            print("\\draw("+str(i)+","+str(j)+")circle(0.2);", file=file_desc);
+
+# init tikz file
+def init_tikz(filename):
+    file_desc=open(filename,"w")
+    print("\\documentclass{standalone}\n\n\\usepackage{tikz}\n\\usepackage{ising}\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()
+
+
+# files
+
+ising=init_tikz("ising.tikz.tex")
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=ising)
+draw_spins(0.5,L,ising)
+close_tikz(ising)
+
+ising_blue=init_tikz("ising_blue.tikz.tex")
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=ising_blue)
+draw_spins(0.1,L,ising_blue)
+close_tikz(ising_blue)
+
+ising_red=init_tikz("ising_red.tikz.tex")
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=ising_red)
+draw_spins(0.9,L,ising_red)
+close_tikz(ising_red)
+
+transfer1=init_tikz("transfer1.tikz.tex")
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=transfer1)
+draw_spins(0.5,1,transfer1)
+close_tikz(transfer1)
+
+transfer2=init_tikz("transfer2.tikz.tex")
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=transfer2)
+draw_spins(0.5,2,transfer2)
+close_tikz(transfer2)
diff --git a/figs/ising.fig/libs/ising.sty b/figs/ising.fig/libs/ising.sty
new file mode 100644
index 0000000..2f8b2fa
--- /dev/null
+++ b/figs/ising.fig/libs/ising.sty
@@ -0,0 +1,9 @@
+% 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);
+  }
+}
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 $(PDFS)
+
+clean: clean-libs clean-aux clean-tex
diff --git a/figs/lieb_lattice.fig/Makefile b/figs/lieb_lattice.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/lieb_lattice.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile
\ No newline at end of file
diff --git a/figs/lieb_lattice.fig/lieb_lattice.tikz.tex b/figs/lieb_lattice.fig/lieb_lattice.tikz.tex
new file mode 100644
index 0000000..e6ef629
--- /dev/null
+++ b/figs/lieb_lattice.fig/lieb_lattice.tikz.tex
@@ -0,0 +1,32 @@
+\documentclass{standalone}
+\usepackage{tikz}
+
+\begin{document}
+\hfil\begin{tikzpicture}
+
+\foreach\i in {0,...,5}{
+  \draw(0,\i)--++(5,0);
+  \draw(\i,0)--++(0,5);
+}
+\foreach\i in {0,...,5}{
+  \foreach\j in {0,...,5}{
+    \fill[color=red](\i,\j)circle(0.1);
+    \draw(\i,\j)circle(0.1);
+  }
+}
+\foreach\i in {0,...,4}{
+  \foreach\j in {0,...,5}{
+    \fill[color=blue](\i+0.5,\j)circle(0.1);
+    \draw(\i+0.5,\j)circle(0.1);
+  }
+}
+\foreach\i in {0,...,5}{
+  \foreach\j in {0,...,4}{
+    \fill[color=blue](\i,\j+0.5)circle(0.1);
+    \draw(\i,\j+0.5)circle(0.1);
+  }
+}
+
+\end{tikzpicture}
+
+\end{document}
diff --git a/figs/nematic.fig/Makefile b/figs/nematic.fig/Makefile
new file mode 100644
index 0000000..8e8462f
--- /dev/null
+++ b/figs/nematic.fig/Makefile
@@ -0,0 +1,15 @@
+PROJECTNAME=nematic
+PNGS=$(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/nematic.fig/nematic-base.gp b/figs/nematic.fig/nematic-base.gp
new file mode 100644
index 0000000..4de0ee2
--- /dev/null
+++ b/figs/nematic.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/nematic.fig/nematic.py b/figs/nematic.fig/nematic.py
new file mode 100644
index 0000000..5c779c0
--- /dev/null
+++ b/figs/nematic.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/plan.fig/Makefile b/figs/plan.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/plan.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile
\ No newline at end of file
diff --git a/figs/plan.fig/plan.tikz.tex b/figs/plan.fig/plan.tikz.tex
new file mode 100644
index 0000000..2241a1d
--- /dev/null
+++ b/figs/plan.fig/plan.tikz.tex
@@ -0,0 +1,34 @@
+\documentclass{standalone}
+\usepackage{tikz}
+\usepackage{color}
+
+\definecolor  {L67}{HTML}{4169E1}
+\definecolor{SML64}{HTML}{4B0082}
+\definecolor {TL71}{HTML}{DAA520}
+\definecolor {HL72}{HTML}{DC143C}
+\definecolor {HL79}{HTML}{32CD32}
+\definecolor  {L89}{HTML}{00CCCC}
+
+\begin{document}
+\hfil\begin{tikzpicture}
+
+\path(0,0)coordinate(L67);
+\path(-1,0.5)coordinate(SML64);
+\path(-2,1)coordinate(TL71);
+\path(0,1)coordinate(HL72);
+\path(0,2)coordinate(HL79);
+\path(1,2.5)coordinate(L89);
+
+\draw(L67)--(SML64)--(TL71);
+\draw(L67)--(HL72)--(HL79)--(L89);
+
+\fill[color=L67](L67)circle(0.15);
+\fill[color=SML64](SML64)circle(0.15);
+\fill[color=TL71](TL71)circle(0.15);
+\fill[color=HL72](HL72)circle(0.15);
+\fill[color=HL79](HL79)circle(0.15);
+\fill[color=L89](L89)circle(0.15);
+
+\end{tikzpicture}
+
+\end{document}
diff --git a/figs/temperley-lieb.fig/Makefile b/figs/temperley-lieb.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/temperley-lieb.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile
\ No newline at end of file
diff --git a/figs/temperley-lieb.fig/tl1.tikz.tex b/figs/temperley-lieb.fig/tl1.tikz.tex
new file mode 100644
index 0000000..6f57aaf
--- /dev/null
+++ b/figs/temperley-lieb.fig/tl1.tikz.tex
@@ -0,0 +1,15 @@
+\documentclass{standalone}
+\usepackage{tikz}
+
+\begin{document}
+\hfil\begin{tikzpicture}
+
+\draw(-1,0)--++(4,0)--++(0,4)--++(-4,0)--cycle;
+
+\draw[line width=4pt](0,0)--++(0,4);
+\draw[line width=4pt](1,0)--++(0,4);
+\draw[line width=4pt](2,0)--++(0,4);
+
+\end{tikzpicture}
+
+\end{document}
diff --git a/figs/temperley-lieb.fig/tl2.tikz.tex b/figs/temperley-lieb.fig/tl2.tikz.tex
new file mode 100644
index 0000000..cc02170
--- /dev/null
+++ b/figs/temperley-lieb.fig/tl2.tikz.tex
@@ -0,0 +1,15 @@
+\documentclass{standalone}
+\usepackage{tikz}
+
+\begin{document}
+\hfil\begin{tikzpicture}
+
+\draw(-1,0)--++(4,0)--++(0,4)--++(-4,0)--cycle;
+
+\draw[line width=4pt](0,0)--++(0,4);
+\draw[line width=4pt](1,0)..controls(1,2)and(2,2)..(2,0);
+\draw[line width=4pt](1,4)..controls(1,2)and(2,2)..(2,4);
+
+\end{tikzpicture}
+
+\end{document}
diff --git a/figs/temperley-lieb.fig/tl3.tikz.tex b/figs/temperley-lieb.fig/tl3.tikz.tex
new file mode 100644
index 0000000..3b92cb5
--- /dev/null
+++ b/figs/temperley-lieb.fig/tl3.tikz.tex
@@ -0,0 +1,15 @@
+\documentclass{standalone}
+\usepackage{tikz}
+
+\begin{document}
+\hfil\begin{tikzpicture}
+
+\draw(-1,0)--++(4,0)--++(0,4)--++(-4,0)--cycle;
+
+\draw[line width=4pt](0,0)..controls(0,2)and(1,2)..(1,0);
+\draw[line width=4pt](0,4)..controls(0,2)and(1,2)..(1,4);
+\draw[line width=4pt](2,0)--++(0,4);
+
+\end{tikzpicture}
+
+\end{document}
diff --git a/figs/temperley-lieb.fig/tl4.tikz.tex b/figs/temperley-lieb.fig/tl4.tikz.tex
new file mode 100644
index 0000000..91fe7c3
--- /dev/null
+++ b/figs/temperley-lieb.fig/tl4.tikz.tex
@@ -0,0 +1,15 @@
+\documentclass{standalone}
+\usepackage{tikz}
+
+\begin{document}
+\hfil\begin{tikzpicture}
+
+\draw(-1,0)--++(4,0)--++(0,4)--++(-4,0)--cycle;
+
+\draw[line width=4pt](0,0)..controls(0,2)and(1,2)..(1,0);
+\draw[line width=4pt](1,4)..controls(1,2)and(2,2)..(2,4);
+\draw[line width=4pt](2,0)..controls(2,2)and(0,2)..(0,4);
+
+\end{tikzpicture}
+
+\end{document}
diff --git a/figs/temperley-lieb.fig/tl5.tikz.tex b/figs/temperley-lieb.fig/tl5.tikz.tex
new file mode 100644
index 0000000..27eb5c5
--- /dev/null
+++ b/figs/temperley-lieb.fig/tl5.tikz.tex
@@ -0,0 +1,15 @@
+\documentclass{standalone}
+\usepackage{tikz}
+
+\begin{document}
+\hfil\begin{tikzpicture}
+
+\draw(-1,0)--++(4,0)--++(0,4)--++(-4,0)--cycle;
+
+\draw[line width=4pt](1,0)..controls(1,2)and(2,2)..(2,0);
+\draw[line width=4pt](0,4)..controls(0,2)and(1,2)..(1,4);
+\draw[line width=4pt](0,0)..controls(0,2)and(2,2)..(2,4);
+
+\end{tikzpicture}
+
+\end{document}