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Diffstat (limited to 'figs/dimer_example.fig/dimer_conf.py')
| -rw-r--r-- | figs/dimer_example.fig/dimer_conf.py | 251 |
1 files changed, 251 insertions, 0 deletions
diff --git a/figs/dimer_example.fig/dimer_conf.py b/figs/dimer_example.fig/dimer_conf.py new file mode 100644 index 0000000..ec27036 --- /dev/null +++ b/figs/dimer_example.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) + |