MC-01 Equilibration

Rule of thumb: All Monte Carlo simulations have to be equilibrated before taking measurements.

Example: Classical Monte Carlo (local updates) simulations

As an example, we will implement a classical Monte Carlo simulation implemented in the Ising model on a finite square lattice of size $48^2$.

Preparing and running the simulation from the command line

The parameter file parm1a:

LATTICE="square lattice"
T=2.269186
J=1
THERMALIZATION=10000
SWEEPS=50000  
UPDATE="local"
MODEL="Ising"
{L=48;}

We first convert the input parameters to XML and then run the application spinmc:

parameter2xml parm1a
spinmc --Tmin 10 --write-xml parm1a.in.xml

Preparing and running the simulation using Python

The following describes what is going on within the script file tutorial1a.py. The headers:

import pyalps

parms = [{
'LATTICE'         : "square lattice",
'MODEL'           : "Ising",
'L'               : 48,
'J'               : 1.,
'T'               : 2.269186,
'THERMALIZATION'  : 10000,
'SWEEPS'          : 50000,
}]

Write into XML input file and run the application spinmc:

input_file = pyalps.writeInputFiles('parm1a',parms)
pyalps.runApplication('spinmc', input_file, Tmin=10, writexml=True)

Evaluating the simulation and preparing plots using Python

The header:

import pyalps;

We first get the list of all result files via:

files = pyalps.getResultFiles(prefix='parm1a')

and then extract, say the timeseries of the |Magnetization| measurements:

ts_M = pyalps.loadTimeSeries(files[0], '|Magnetization|');

We can then visualize graphically:

import matplotlib.pyplot as plt
plt.plot(ts_M)
plt.show()

Based on the timeseries, the user will then judge for himself/herself whether the simulation has reached equilibration.

A convenient tool: pyalps.checkSteadyState

ALPS Python provides a convenient tool to check whether a measurement observable(s) has (have) reached steady state equilibrium. Read here to see how it works. Here is an example (observable: |Magnetization|) (default: 68.27% confidence interval):

import pyalps
data = pyalps.loadMeasurements(pyalps.getResultFiles(prefix='parm1a'), '|Magnetization|');
data = pyalps.checkSteadyState(data);

and if you want a 90% confidence interval:

data = pyalps.checkSteadyState(data, confidenceInterval=0.9);

Setting up and running the simulation in Vistrails

To run the simulation in Vistrails open the file mc-01b-equilibration-and-convergence.vt.

Convergence

Here, we use the same example in the previous section.

Using Python

Implementation in Python is straightforward.

import pyalps
data = pyalps.loadMeasurements(pyalps.getResultFiles(prefix='parm1a'), '|Magnetization|');
data = pyalps.checkConvergence(data);

Setting up and running the simulation in Vistrails

To run the simulation in Vistrails open the file mc-01b-equilibration-and-convergence.vt.

Contributors

• Matthias Troyer
• Ping Nang Ma