Work

Comparison of Swendsen‐Wang and heat‐bath dynamics

Year: 2012

Type: article

Abstract: We prove that the spectral gap of the Swendsen‐Wang process for the Potts model on graphs with bounded degree is bounded from below by some constant times the spectral gap of any single‐spin dynamics. This implies rapid mixing for the two‐dimensional Potts model at all temperatures above the critical one, as well as rapid mixing at the critical temperature for the Ising model. After this we introduce a modified version of the Swendsen‐Wang algorithm for planar graphs and prove rapid mixing for the two‐dimensional Potts models at all non‐critical temperatures. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 42, 520–535, 2013

Source: Random Structures and Algorithms

DOI: 10.1002/rsa.20431

Author: Mario Ullrich

Institution: Friedrich Schiller University Jena

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Award: G8245911196