The Wolff algorithm,
named after
Ulli Wolff, is an
algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
for
Monte Carlo simulation of the
Ising model and
Potts model in which the unit to be flipped is not a single spin (as in the
heat bath or
Metropolis algorithms) but a cluster of them. This cluster is defined as the set of connected spins sharing the same spin states, based on the
Fortuin-Kasteleyn representation.
The Wolff algorithm is similar to the
Swendsen–Wang algorithm, but different in that the former only flips one randomly chosen cluster with probability 1, while the latter flip every cluster independently with probability 1/2. It is shown numerically that flipping only one cluster decreases the
autocorrelation
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable ...
time of the spin statistics.
The advantage of Wolff algorithm over other algorithms for magnetic spin simulations like single spin flip is that it allows non-local moves on the energy. One important consequence of this is that in some situations (e.g. ferromagnetic Ising model or fully frustrated Ising model), the scaling of the Multicanonic simulation is
, better than
, where z is the exponent associated with the critical slowing down phenomena.
References
*
*
*
External links
''Cluster Algorithms''at
Netlib
*Implementation in Julia: https://github.com/cossio/SquareIsingModel.jl
Monte Carlo methods
Statistical mechanics
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