#!/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]=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) # 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) # 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 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)