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

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 $\beta \to \infty$ 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.

pg. 50, fig. 15. In this paper we consider, with the same authors, the same model as our previous work arXiv:2105.14335v2, but in a complementary range of parameter values. Thus we write an admin note by marking any known overlaps in advance: sections 1, 2, 3 and appendix in the present paper have some substantial overlap to sections 1, 2, 3 and 5 in the previous paper arXiv:2105.14335v2. arXiv admin note: This version is different than other versions of this paper, and readers should refer to arXiv:2105.14335 for the negative external magnetic field model

References in corpus (11)

• Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model
• Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States
• Metastability for the degenerate Potts Model with negative external magnetic field under Glauber dynamics
• Ising model on clustered networks: A model for opinion dynamics
• Critical Droplets and sharp asymptotics for Kawasaki dynamics with weakly anisotropic interactions. Extended version
• Metastability of the Potts ferromagnet on random regular graphs
• Metastability in a lattice gas with strong anisotropic interactions under Kawasaki dynamics
• Critical Droplets and sharp asymptotics for Kawasaki dynamics with strongly anisotropic interactions
• Metastability for Kawasaki dynamics on the hexagonal lattice
• Metastability of synchronous and asynchronous dynamics
• Metastability of the three-state Potts model with general interactions

Cited by in corpus (1)

• Critical configurations of the hard-core model on square grid graphs