We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants Jij > 0, where i, j ∈ {1, 2, 3} are the possible spin values (or colors). The resulting energy landscape is thus significantly more complex than in the original Ising or Potts models. The system evolves according to a Glauber-type spin-flipping dynamics. We focus on a region of the parameter space where there are two symmetric metastable states and a stable state, and the height of a direct path between the metastable states is equal to the height of a direct path between any metastable state and the stable state. We study the metastable transition time in probability and in expectation, the mixing time of the dynamics and the spectral gap of the system when the inverse temperature β tends to infinity. Then, we identify all the critical configurations that are visited with high probability during the metastable transition. Our main tool is the so-called pathwise approach to metastability, which requires a detailed analysis of the energy landscape.

Metastability of the three-state Potts model with general interactions / Gianmarco Bet, Anna Gallo, Seonwoo Kim. - In: ELECTRONIC JOURNAL OF PROBABILITY. - ISSN 1083-6489. - ELETTRONICO. - 28:(2023), pp. 0-0. [10.1214/23-EJP1003]

Metastability of the three-state Potts model with general interactions

Gianmarco Bet;
2023

Abstract

We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants Jij > 0, where i, j ∈ {1, 2, 3} are the possible spin values (or colors). The resulting energy landscape is thus significantly more complex than in the original Ising or Potts models. The system evolves according to a Glauber-type spin-flipping dynamics. We focus on a region of the parameter space where there are two symmetric metastable states and a stable state, and the height of a direct path between the metastable states is equal to the height of a direct path between any metastable state and the stable state. We study the metastable transition time in probability and in expectation, the mixing time of the dynamics and the spectral gap of the system when the inverse temperature β tends to infinity. Then, we identify all the critical configurations that are visited with high probability during the metastable transition. Our main tool is the so-called pathwise approach to metastability, which requires a detailed analysis of the energy landscape.
2023
28
0
0
Gianmarco Bet, Anna Gallo, Seonwoo Kim
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1331678
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