Wang-Landau method

The Wang-Landau method was proposed by F. Wang and D. P. Landau (Ref. 1) to compute the density of states, $\Omega (E)$ , of Potts models; where $\Omega (E)$ is the number of microstates of the system having energy $E$ .

The Wang-Landau method in its original version is a simulation technique designed to reach an uniform sampling of the energies of the system in a given range. In a standard Metropolis Monte Carlo in the canonical ensemble the probability of a given microstate, $X$ is given by:

$P(X)\propto \exp \left[-E(X)/k_{B}T\right]$ ;

whereas for the Wang-Landau procedure we can write:

$P(X)\propto \exp \left[-f(E(x))\right]$ ;

where $f(E)$ is a function of the energy. $f(E)$ changes during the simulation in order get a prefixed distribution of energies (usually a uniform distribution); this is done by modifying the values of $f(E)$ to reduce the probability of the energies that have been already visited.

References

Wang-Landau method

References

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