Rapid Mixing of Glauber Dynamics of Gibbs Ensembles via Aggregate Path Coupling and Large Deviations Methods

• Published in: Journal of statistical physics Vol. 161; no. 3; pp. 553 - 576
• Main Authors: Kovchegov, Yevgeniy, Otto, Peter T.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2015; Springer
• Subjects: Mathematical and Computational Physics; Physical Chemistry; Physics; Physics and Astronomy; Quantum Physics; Statistical Physics and Dynamical Systems; Theoretical; Mixing times; Primary 60J10; Curie–Weiss–Potts model; Gibbs ensemble; Path coupling; Glauber dynamics; Secondary 60K35; Equilibrium phase transition
• ISSN: 0022-4715; 1572-9613
• DOI: 10.1007/s10955-015-1345-3

In this paper, we present a novel extension to the classical path coupling method to statistical mechanical models which we refer to as aggregate path coupling. In conjunction with large deviations estimates, we use this aggregate path coupling method to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibit discontinuous phase transitions which have traditionally been more difficult to analyze rigorously. The parameter region for rapid mixing for the generalized Curie–Weiss–Potts model is derived as a new application of the aggregate path coupling method.