Single-cluster Monte Carlo dynamics for the Ising model

1572-9613

Cluster acceleration ; critical slowing down ; Swendsen-Wang algorithm ; Wolff algorithm ; Fortuin-Kasteleyn mapping ; Coniglio-Klein clusters

Springer Online Journal Archives 1860-2000

Physics

Abstract We present an extensive study of a new Monte Carlo acceleration algorithm introduced by Wolff for the Ising model. It differs from the Swendsen-Wang algorithm by growing and flipping single clusters at a random seed. In general, it is more efficient than Swendsen-Wang dynamics ford〉2, giving zero critical slowing down in the upper critical dimension. Monte Carlo simulations give dynamical critical exponentsz w=0.33±0.05 and 0.44+0.10 ind=2 and 3, respectively, and numbers consistent withz w=0 ind=4 and mean-field theory. We present scaling arguments which indicate that the Wolff mechanism for decorrelation differs substantially from Swendsen-Wang despite the apparent similarities of the two methods.

Electronic Resource