# ALPS 2 Tutorials:MC-01 Equilibration

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# 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 482.

### Using 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


Add in timeseries analysis here after Python

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

### Using Python

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

The headers:

import pyalps


Set up a python list of parameters (python) dictionaries:

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


Write into XML input file:

input_file = pyalps.writeInputFiles('parm1a',parms)


and run the application spinmc:

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


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: steady_state_check

ALPS Python provides a convenient tool to check whether a measurement observable(s) has (have) reached steady state equilibrium.

Here is one example:

pyalps.steady_state_check(files[0], 'Density')


and another one:

pyalps.steady_state_check(files[0], ['Density', 'Energy Density'])


Description
1. steady_state_check first performs a linear fit on the timeseries, and decides whether the measurement observable has reached steady state equilibrium based on the gradient/slope of the fitted line.

2. The optional arguments of steady_state_check are:

 argument default remark tolerance 0.01 $\mathrm{tolerance} = \frac{X^\mathrm{(fit)} (t_\mathrm{final}) - X^\mathrm{(fit)} (t_\mathrm{initial})}{\bar{X}}$ simplified False shall we combine the checks of all observables as 1 final boolean answer? includeLog False shall we print the detailed log?

3. To see the complete log for instance:

pyalps.steady_state_check(files[0], ['Density', 'Energy Density'], includeLog=True)


### Using Vistrails

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