Wolff algorithm

The Wolff algorithm, named after Ulli Wolff, is an algorithm for Monte Carlo simulation of the Ising 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 neighbouring spins sharing the same value of the spin. The Wolff algorithm is an improvement over the Swendsen–Wang algorithm because it has a larger probability of flipping bigger clusters.

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 $N^{{2+z}}$, where z is the exponent associated with the critical slowing down phenomena.

References

• Wolff, Ulli (1989), "Collective Monte Carlo Updating for Spin Systems", Physical Review Letters, 62 (4): 361, Bibcode:1989PhRvL..62..361W, doi:10.1103/PhysRevLett.62.361, PMID 10040213
• Bae, S.; Ko, S.H.; Coddington, P.D. (1995), "Parallel Wolff cluster algorithms", International Journal of Modern Physics C, 6 (2): 197, Bibcode:1995IJMPC...6..197B, doi:10.1142/S0129183195000150
• Ferrenberg, Alan M.; Landau, D.P.; Wong, Y. Joanna (1992), "Monte Carlo simulations: Hidden errors from good random number generators", Physical Review Letters, 69 (23): 3382, Bibcode:1992PhRvL..69.3382F, doi:10.1103/PhysRevLett.69.3382, PMID 10046804

External links

• Cluster Algorithms at Netlib