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| -rw-r--r-- | Jauslin_SMM118_2017.tex | 140 | ||||
| -rw-r--r-- | Makefile | 50 | ||||
| -rw-r--r-- | README | 39 | ||||
| -rw-r--r-- | figs/atoms.fig/Makefile | 15 | ||||
| -rw-r--r-- | figs/atoms.fig/nematic-base.gp | 21 | ||||
| -rw-r--r-- | figs/atoms.fig/nematic.py | 90 | ||||
| -rw-r--r-- | figs/dimer_example.fig/Makefile | 32 | ||||
| -rw-r--r-- | figs/dimer_example.fig/dimer_conf.py | 235 | ||||
| l--------- | figs/dimer_example.fig/libs/dimer.sty | 1 | ||||
| -rw-r--r-- | figs/libs/Makefile | 25 | ||||
| -rw-r--r-- | figs/libs/dimer.sty | 33 | ||||
| -rw-r--r-- | libs/ian-presentation.cls | 187 |
12 files changed, 868 insertions, 0 deletions
diff --git a/Jauslin_SMM118_2017.tex b/Jauslin_SMM118_2017.tex new file mode 100644 index 0000000..f383ee8 --- /dev/null +++ b/Jauslin_SMM118_2017.tex @@ -0,0 +1,140 @@ +\documentclass{ian-presentation} + +\usepackage[hidelinks]{hyperref} +\usepackage{graphicx} +\usepackage{dsfont} + +\begin{document} +\pagestyle{empty} +\hbox{}\vfil +\bf\Large +\hfil Nematic liquid crystal phase\par +\smallskip +\hfil in a system of interacting dimers\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} +\vfill +\eject + +\title{Models} +\begin{itemize} + \item (Disertori, Giuliani, Jauslin): hard plates in $\mathbb R^3$. + \item \href{http://dx.doi.org/10.1007/s00220-013-1767-1}{[Disertori, Giuliani, 2013]}: hard rods in $\mathbb Z^2$. + \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/BF00535264}{[Bricmont, Kuroda, Lebowitz, 1984]}: hard needles in $\mathbb R^2$. + %\item \href{http://dx.doi.org/10.1007/s10955-015-1421-8}{[Alberici, 2016]}: different fugacities for horizontal and vertical dimers. + %\item \href{http://dx.doi.org/10.1103/PhysRevB.89.035128}{[Papanikolaou, Charrier, Fradkin, 2014]}: numerics. + \item \href{http://dx.doi.org/10.1007/BF01009518}{[Heilmann, Lieb, 1979]}: interacting dimers. +\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{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 + +\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) $(SYNCTEXS) + +clean: clean-aux clean-tex clean-libs clean-figs @@ -0,0 +1,39 @@ +This directory contains the source files to typeset the presentation, and +generate the figures. This can be accomplished by running + make + +This document uses a custom class file, located in the 'libs' directory, which +defines a number of commands. + + +* Dependencies: + + pdflatex + TeXlive packages: + amsfonts + graphics + hyperref + latex + pgf + standalone + GNU make + +* Files: + + Jauslin_SMM118_2017.tex: + main LaTeX file + + libs: + custom LaTeX class file + + figs: + source code for the figures + + figs/dimer_example.fig/dimer_conf.py: + this python script randomly generates a suitable dimer configuration for + the figures grid.pdf, dimers.pdf and interaction.pdf, boundary.pdf and + dimer_contour.pdf + + figs/atoms.fig/nematic.py: + this python script randomly generates configurations of non-overlapping + ellipsoids for the figure nematic.png. diff --git a/figs/atoms.fig/Makefile b/figs/atoms.fig/Makefile new file mode 100644 index 0000000..8e8462f --- /dev/null +++ b/figs/atoms.fig/Makefile @@ -0,0 +1,15 @@ +PROJECTNAME=nematic +PNGS=$(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/atoms.fig/nematic-base.gp b/figs/atoms.fig/nematic-base.gp new file mode 100644 index 0000000..92ffc4d --- /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") + +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..386ecd1 --- /dev/null +++ b/figs/dimer_example.fig/Makefile @@ -0,0 +1,32 @@ +PROJECTNAME=grid dimers interaction +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..f8838bd --- /dev/null +++ b/figs/dimer_example.fig/dimer_conf.py @@ -0,0 +1,235 @@ +#!/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) + 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..7d8331b --- /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{240pt} +\setlength\paperwidth{320pt} + +%% 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=272pt +\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 |