Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics

DOI10.1016/J.SPA.2024.104343arXiv2108.04011MaRDI QIDQ6374837

F. R. Nardi, Gianmarco Bet, Anna Chiara Gallo

Publication date: 3 August 2021

Abstract: We consider the ferromagnetic q-state Potts model on a finite grid graph with non-zero external field and periodic boundary conditions. The system evolves according to Glauber-type dynamics described by the Metropolis algorithm, and we focus on the low temperature asymptotic regime. We analyze the case of positive external magnetic field. In this energy landscape there are

1

stable configuration and

q - 1

metastable states. We study the asymptotic behavior of the first hitting time from any metastable state to the stable configuration as

in probability, in expectation, and in distribution. We also identify the exponent of the mixing time and find an upper and a lower bound for the spectral gap. We also geometrically identify the union of all minimal gates and the tube of typical trajectories for the transition from any metastable state to the unique stable configuration.

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20)