Wolff algorithm: Difference between revisions

Revision as of 04:34, 18 April 2021

Revision as of 17:07, 22 April 2021

Line 1:

The '''Wolff algorithm''',<ref>{{Cite journal|last=Wolff|first=Ulli|date=1989-01-23|title=Collective Monte Carlo Updating for Spin Systems|url=https://link.aps.org/doi/10.1103/PhysRevLett.62.361|journal=Physical Review Letters|volume=62|issue=4|pages=361–364|doi=10.1103/PhysRevLett.62.361}}</ref>, named after [[Ulli Wolff]], is an [[algorithm]] 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 [[Glauber dynamics|heat bath]] or [[Metropolis–Hastings algorithm|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 [[Random cluster model|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.