Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited

Abstract

We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts model. We find that the Li-Sokal bound (${\tau }_{int,E}\ge const\times C_H$) is almost but not quite sharp. The ratio ${\tau }_{int,E}/C_H$ seems to diverge either as a small power ($\approx 0.08$) or as a logarithm.

35 pages including 3 figures. Self-unpacking file containing the LaTeX file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and eqsection.sty) and the 3 Postscript figures. Revised version fixes a normalization error in ξ(with many thanks to Wolfhard Janke for finding the error!). To be published in J. Stat. Phys. 87, no. 1/2 (April 1997)

References in corpus (3)

• Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
• Dynamic Critical Behavior of a Swendsen-Wang-Type Algorithm for the Ashkin-Teller Model
• Dynamic Critical Behavio(u)r of a Cluster Algorithm for the Ashkin--Teller Model

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• Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
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• Density Profiles, Casimir Amplitudes and Critical Exponents in the Two Dimensional Potts Model: A Density Matrix Renormalization Study
• Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm
• Phase transition in the 3-state Potts antiferromagnet on the diced lattice
• Local and cluster critical dynamics of the 3d random-site Ising model
• Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model. I. Two Dimensions
• The three-state Potts antiferromagnet on plane quadrangulations
• Identifying the Huse-Fisher universality class of the three-state chiral Potts model
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• The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
• Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations
• Critical Nonequilibrium Cluster-flip Relaxations in Ising Models
• Bridges in the random-cluster model
• A cluster algorithm for Potts models with fixed spin densities
• Dynamic critical behavior of cluster algorithms for 2D Ashkin-Teller and Potts models
• Aging and stationary properties of non-equilibrium symmetrical three-state models
• Numerical simulation study of the dynamical behavior of the Niedermayer algorithm
• Critical dynamics of two-replica cluster algorithms
• Exploring the worldline formulation of the Potts model
• Dynamical behavior of the Niedermayer algorithm applied to Potts models