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 The Ising model () (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent ...

and

Potts model In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. By studying the Potts model, one may gain insight into the behaviour of ferromagnets and certain other phenom ...

in which the unit to be flipped is not a single spin (as in the

heat bath In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...

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 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

N^2

, better than

N^

, 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 {{statisticalmechanics-stub