User:Jackliddle/Metropolis algorithm

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

The algorithm is widely used in lattice gauge theory.

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[edit] Description

For generating a sequence of field configurations Σ 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 Σ giving us a new configuation Σ' there is a corresponding change in the action.

ΔS = S(Σ') − S(Σ)

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