The Annals of Applied Probability

Random cluster dynamics for the Ising model is rapidly mixing

Heng Guo and Mark Jerrum

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We show that the mixing time of Glauber (single edge update) dynamics for the random cluster model at $q=2$ on an arbitrary $n$-vertex graph is bounded by a polynomial in $n$. As a consequence, the Swendsen–Wang algorithm for the ferromagnetic Ising model at any temperature also has a polynomial mixing time bound.

Article information

Ann. Appl. Probab., Volume 28, Number 2 (2018), 1292-1313.

Received: December 2016
Revised: April 2017
First available in Project Euclid: 11 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 68W20: Randomized algorithms
Secondary: 68Q87: Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also 68W20, 68W40]

Random cluster Markov chains Ising model Swendsen–Wang dynamics


Guo, Heng; Jerrum, Mark. Random cluster dynamics for the Ising model is rapidly mixing. Ann. Appl. Probab. 28 (2018), no. 2, 1292--1313. doi:10.1214/17-AAP1335.

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