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Dynamic Critical Behavior of the Chayes–Machta Algorithm for the Random-Cluster Model, I. Two Dimensions

  • Timothy M. Garoni
  • Giovanni Ossola
  • Marco Polin
  • Alan D. Sokal
Article

Abstract

We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes–Machta dynamics for the Fortuin–Kasteleyn random-cluster model, which generalizes the Swendsen–Wang dynamics for the q-state Potts ferromagnet to non-integer q≥1. We consider spatial dimension d=2 and 1.25≤q≤4 in steps of 0.25, on lattices up to 10242, and obtain estimates for the dynamic critical exponent z CM. We present evidence that when 1≤q≲1.95 the Ossola–Sokal conjecture z CMβ/ν is violated, though we also present plausible fits compatible with this conjecture. We show that the Li–Sokal bound z CMα/ν is close to being sharp over the entire range 1≤q≤4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.

Keywords

Random-cluster model Potts model Chayes–Machta algorithm Swendsen–Wang algorithm Cluster algorithm Dynamic critical behavior 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Timothy M. Garoni
    • 1
    • 5
  • Giovanni Ossola
    • 2
  • Marco Polin
    • 3
  • Alan D. Sokal
    • 4
    • 6
  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneMelbourneAustralia
  2. 2.Department of PhysicsNew York City College of TechnologyBrooklynUSA
  3. 3.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK
  4. 4.Department of PhysicsNew York UniversityNew YorkUSA
  5. 5.School of Mathematical SciencesMonash UniversityMelbourneAustralia
  6. 6.Department of MathematicsUniversity College LondonLondonUK

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