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

Francesca R. Nardi, Alessandro Zocca*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

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 β. Our analysis concerns the low-temperature regime β→∞, 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 β→∞ in probability, in expectation, and in distribution and obtaining tight bounds on the mixing time as side-result.

Original languageEnglish
Pages (from-to)4556-4575
Number of pages20
JournalStochastic Processes and Their Applications
Volume129
Issue number11
DOIs
Publication statusPublished - 1 Nov 2019
Externally publishedYes

Keywords

  • Glauber dynamics
  • Grid graphs
  • Hitting times
  • Ising model
  • Mixing time
  • Potts model

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