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 language | English |
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Pages (from-to) | 4556-4575 |
Number of pages | 20 |
Journal | Stochastic Processes and Their Applications |
Volume | 129 |
Issue number | 11 |
DOIs | |
Publication status | Published - 1 Nov 2019 |
Externally published | Yes |
Keywords
- Glauber dynamics
- Grid graphs
- Hitting times
- Ising model
- Mixing time
- Potts model