Wolff algorithm: Difference between revisions

Revision as of 04:34, 18 April 2021

Latest revision as of 14:57, 24 June 2025

(6 intermediate revisions by 5 users not shown)

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|pmid=10040213|bibcode=1989PhRvL..62..361W |url-access=subscription}}</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.

Line 6:

==References==

{{Reflist}}

*{{citation | doi=10.1103/PhysRevLett.62.361 | title=Collective Monte Carlo Updating for Spin Systems | year=1989 | author=Wolff, Ulli | journal=Physical Review Letters | volume=62 | pages=361–364 | pmid=10040213 | issue=4 | bibcode=1989PhRvL..62..361W}}

*{{citation | doi=10.1142/S0129183195000150 | title=Parallel Wolff cluster algorithms | year=1995 | author1=Bae, S. | author2=Ko, S.H. | author3=Coddington, P.D. | journal=International Journal of Modern Physics C | volume=6 | issue=2 | pages=197 |bibcode = 1995IJMPC...6..197B | citeseerx=10.1.1.138.1448 }}

Line 12 ⟶ 13:

==External links==

*[http://www.netlib.org/utk/lsi/pcwLSI/text/node292.html ''Cluster Algorithms''] at [[Netlib]]

*Implementation in Julia: https://github.com/cossio/SquareIsingModel.jl

[[Category:Monte Carlo methods]]

Line 17 ⟶ 19:

{{physicsstatisticalmechanics-stub}}