User:Jackliddle/Metropolis algorithm

The Metropolis Algorithm is used in the Monte Carlo methods for importance sampling probablity distributions.

The algorithm is widely used in lattice gauge theory.

Description

For generating a sequence of field configurations $\mathrm{\Sigma }$ distributed with a probability density $e^{-S}$. Expectation values of Quantum Mechanical observables can then be calculated

$<O>=\frac{1}{n}\sum _{i=m+1}^{m+n}O({\mathrm{\Sigma }}_i)$

where the first m steps bring the system into equilbrium.

If we change one link in the field configuration $\mathrm{\Sigma }$ giving us a new configuation ${\mathrm{\Sigma }}^{\prime }$ there is a corresponding change in the action.

$\mathrm{\Delta }S=S({\mathrm{\Sigma }}^{\prime })-S(\mathrm{\Sigma })$

Pseudo Code

using Wikicode

See also

• Metropolis-Hastings algorithm