298 lines
9.4 KiB
Python
298 lines
9.4 KiB
Python
#!/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)
|
|
|
|
# find interactions with boundary
|
|
def boundary_interactions(dimers,rho):
|
|
out=[]
|
|
for d in dimers:
|
|
for v in rho:
|
|
if(d[0]==v[0] and d[1]==v[1]):
|
|
out.append([d[0],d[1]-1])
|
|
elif(d[0]==v[0] and d[1]==v[1]-1):
|
|
out.append([d[0],d[1]+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 magnetized part of boundary
|
|
def draw_boundary(rho, file_desc):
|
|
for v in rho:
|
|
print("\\fill[color=red]("+str(v[0])+","+str(v[1])+")circle(10pt);", 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")
|
|
|
|
# magnetized part of the boundary
|
|
rho=[]
|
|
for i in range(0,L):
|
|
if(random.randint(0,1)==0):
|
|
rho.append([i,0])
|
|
if(random.randint(0,1)==0):
|
|
rho.append([i,L-1])
|
|
|
|
|
|
# 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)
|
|
|
|
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)
|
|
draw_boundary(rho,boundary)
|
|
print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=boundary)
|
|
draw_interactions(boundary_interactions(v_dimers,rho),[],boundary)
|
|
draw_dimers(v_dimers+v_mantle,h_dimers+h_mantle,boundary,"black")
|
|
close_tikz(boundary)
|
|
|
|
bounding_loop=init_tikz("bounding_loop.tikz.tex")
|
|
print("\\begin{scope}", file=bounding_loop)
|
|
print(" \\clip", end="", file=bounding_loop)
|
|
for e in loop1:
|
|
print("("+str(e[0])+","+str(e[1])+")--", end="", file=bounding_loop)
|
|
print("cycle;",file=bounding_loop)
|
|
print(" \\fill[color=cyan]("+str(mu-2*l0-2)+","+str(mu-7)+")--++("+str(4*l0+3)+",0)--++(0,13)--++("+str(-4*l0-3)+",0);", file=bounding_loop)
|
|
print(" \\fill[color=red]", end="", file=bounding_loop)
|
|
for e in core_loop1:
|
|
print("("+str(e[0])+","+str(e[1])+")--", end="", file=bounding_loop)
|
|
print("cycle;",file=bounding_loop)
|
|
print("\\end{scope}\n", file=bounding_loop)
|
|
print("\\grid{"+str(4*l0+3)+"}{"+str(13)+"}{("+str(mu-2*l0-2)+","+str(mu-7)+")}\n", file=bounding_loop)
|
|
draw_loops([loop1],bounding_loop,"black")
|
|
close_tikz(bounding_loop)
|
|
|
|
loops=init_tikz("dimer_loops.tikz.tex")
|
|
print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=loops)
|
|
draw_loops([loop1,loop2,loop3],loops,"blue")
|
|
draw_interactions(v_interactions,h_interactions,loops)
|
|
draw_dimers(v_dimers,h_dimers,loops,"black")
|
|
draw_dimers(v_mantle,h_mantle,loops,"gray")
|
|
close_tikz(loops)
|
|
|
|
contour=init_tikz("dimer_contour.tikz.tex")
|
|
print("\\draw[color=green, line width=15pt]("+str(mu-2-0.5)+","+str(mu+1)+")--++(1,0);", file=contour)
|
|
print("\\draw[color=green, line width=15pt]("+str(mu-2-0.5)+","+str(mu+2)+")--++(1,0);", file=contour)
|
|
print("\\draw[color=green, line width=15pt]("+str(mu-0.5)+","+str(mu+1)+")--++(2,0);", file=contour)
|
|
print("\\draw[color=green, line width=15pt]("+str(mu-0.5)+","+str(mu+2)+")--++(2,0);", file=contour)
|
|
print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=contour)
|
|
draw_loops([loop1,loop2],contour,"green")
|
|
draw_loops([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,"gray")
|
|
close_tikz(contour)
|
|
|