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

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

where the first m steps bring the system into equilbrium.

If we change one link in the field configuration $\Sigma$ giving us a new configuation $\Sigma '$ there is a corresponding change in the action.

$\Delta S=S(\Sigma ')-S(\Sigma )$

Pseudo Code

using Wikicode

See also

• Metropolis-Hastings algorithm