We consider the ferromagnetic q-state Potts model with zero external field in a finite volume evolving according to Glauber-type dynamics described by the Metropolis algorithm in the low temperature asymptotic limit. Our analysis concerns the multi-spin system that has q stable equilibria. Focusing on grid graphs with periodic boundary conditions, we study the tunneling between two stable states and from one stable state to the set of all other stable states. In both cases we identify the set of gates for the transition and prove that this set has to be crossed with high probability during the transition. Moreover, we identify the tube of typical paths and prove that the probability to deviate from it during the transition is exponentially small.

Critical configurations and tube of typical trajectories for the Potts and Ising models with zero external field / Gianmarco Bet; Anna Gallo; Francesca Romana Nardi. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - ELETTRONICO. - (2021), pp. 0-0. [10.1007/s10955-021-02814-1]

Critical configurations and tube of typical trajectories for the Potts and Ising models with zero external field

Gianmarco Bet
Membro del Collaboration Group
;
Anna Gallo
Membro del Collaboration Group
;
Francesca Romana Nardi
Membro del Collaboration Group
2021

Abstract

We consider the ferromagnetic q-state Potts model with zero external field in a finite volume evolving according to Glauber-type dynamics described by the Metropolis algorithm in the low temperature asymptotic limit. Our analysis concerns the multi-spin system that has q stable equilibria. Focusing on grid graphs with periodic boundary conditions, we study the tunneling between two stable states and from one stable state to the set of all other stable states. In both cases we identify the set of gates for the transition and prove that this set has to be crossed with high probability during the transition. Moreover, we identify the tube of typical paths and prove that the probability to deviate from it during the transition is exponentially small.
2021
0
0
Goal 17: Partnerships for the goals
Gianmarco Bet; Anna Gallo; Francesca Romana Nardi
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1227442
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