The aggregate path coupling method for the Potts model on bipartite graph

Author(s)

Hernandez, Jose C. ; Kovchegov, Yevgeniy ; Otto, Peter T.

• Document type: Journal article
• Source: Journal of Mathematical Physics; v. 58, n. 2 FEB 2017.
• Web of Science Citations: 0

Abstract

In this paper, we derive the large deviation principle for the Potts model on the complete bipartite graph K-n,K-n as n increases to infinity. Next, for the Potts model on K-n,K-n, we provide an extension of the method of aggregate path coupling that was originally developed in the work of Kovchegov, Otto, and Titus {[}J. Stat. Phys. 144(5), 10091027 (2011)] for the mean-field Blume-Capel model and in Kovchegov and Otto {[}J. Stat. Phys. 161(3), 553-576 (2015)] for a general mean-field setting that included the generalized Curie-Weiss-Potts model analyzed in the work of Jahnel et al. {[}Markov Process. Relat. Fields 20, 601-632 (2014)]. We use the aggregate path coupling method to identify and determine the threshold value beta(s) separating the rapid and slow mixing regimes for the Glauber dynamics of the Potts model on K-n,K-n. Published by AIP Publishing. (AU)

• FAPESP's process: 15/16407-8 - Phase transition and critical phenomena in two-dimensional discrete quantum gravity
• Grantee: José Javier Cerda Hernández
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor