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

Francesca R. Nardi and Alessandro Zocca

Stochastic Processes and their Applications, 2019, vol. 129, issue 11, 4556-4575

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.

Keywords: Ising model; Potts model; Glauber dynamics; Hitting times; Mixing time; Grid graphs (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:11:p:4556-4575

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DOI: 10.1016/j.spa.2018.12.001

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