Tunneling behavior of Ising and Potts models in the low-temperature regime

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Nardi, Francesca R.¹  Zocca, Alessandro² 

[1] Univ Florence, Dept Math & Comp Sci, I-50134 Florence, Italy

[2] CALTECH, Dept Comp & Math Sci, Pasadena, CA 91125 USA

关键词: Ising model;    Potts model;    Glauber dynamics;    Hitting times;    Mixing time;    Grid graphs;   

DOI  :  10.1016/j.spa.2018.12.001

来源: Elsevier

【 摘 要 】

We consider the ferromagnetic q-state Potts model with zero external field in a finite volume and assume that its stochastic evolution is described by a Glauber-type dynamics parametrized by the inverse temperature beta. Our analysis concerns the low-temperature regime beta -> infinity, in which this multi-spin system has q stable equilibria. Focusing on grid graphs with various boundary conditions, we study the tunneling phenomena of the q-state Potts model, characterizing the asymptotic behavior of the first hitting times between stable equilibria as beta -> infinity in probability, in expectation, and in distribution and obtaining tight bounds on the mixing time as side-result. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free