Running Classic Monte Carlo
As a simple example for classic Monte Carlo we consider obtaining a phase transition in 2D Ising model.
First, we need to import required packages.
import pyalps
import matplotlib.pyplot as plt
import pyalps.plotThen we prepare the input parameters. Here we consider lattices of sizes $4\times 4$, $8\times 8$, $16\times 16$, for different temperatures.
parms = []
for l in [4,8,16]:
for t in [5.0,4.5,4.0,3.5,3.0,2.9,2.8,2.7]:
parms.append(
{
'LATTICE' : "square lattice",
'T' : t,
'J' : 1 ,
'THERMALIZATION' : 1000,
'SWEEPS' : 400000,
'UPDATE' : "cluster",
'MODEL' : "Ising",
'L' : l
}
)
for t in [2.6, 2.5, 2.4, 2.3, 2.2, 2.1, 2.0, 1.9, 1.8, 1.7, 1.6, 1.5, 1.2]:
parms.append(
{
'LATTICE' : "square lattice",
'T' : t,
'J' : 1,
'THERMALIZATION' : 1000,
'SWEEPS' : 40000,
'UPDATE' : "cluster",
'MODEL' : "Ising",
'L' : l
}
)After that, we write the input into the format ALPS expects using Python, and tell it to run a spin Monte Carlo simulation (spinmc) using the input file:
#write the input file and run the simulation
input_file = pyalps.writeInputFiles('parm7a',parms)
pyalps.runApplication('spinmc',input_file,Tmin=5)After the simulation is finished, we can evaluate and plot the results.
pyalps.evaluateSpinMC(pyalps.getResultFiles(prefix='parm7a'))
#load the susceptibility and collect it as function of temperature T
data = pyalps.loadMeasurements(pyalps.getResultFiles(prefix='parm7a'),['|Magnetization|'])
magnetization_abs = pyalps.collectXY(data,x='T',y='|Magnetization|',foreach=['L'])
#make plots
plt.figure()
pyalps.plot.plot(magnetization_abs)
plt.xlabel('Temperature $T$')
plt.ylabel('Magnetization $|m|$')
plt.title('2D Ising model')
plt.show()We should obtain the following figure for magnetization in the 2D Ising model:
