Metastability for the Ising model on the hexagonal lattice

2021/01/28 by Valentina Apollonio, Apollonio, Valentina, Vanessa Jacquier +5 · 1 citation
Mathematics · Physics and Astronomy · #05B45 #60J10 #60J45 #82C20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2101.11894

openalex publication_date 2021/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Ising model on the hexagonal lattice evolving according to Metropolis dynamics. We study its metastable behavior in the limit of vanishing temperature when the system is immersed in a small external magnetic field. We determine the asymptotic properties of the transition time from the metastable to the stable state up to a multiplicative factor and study the mixing time and the spectral gap of the Markov process. We give a geometrical description of the critical configurations and show how not only their size but their shape varies depending on the thermodynamical parameters. Finally we provide some results concerning polyiamonds of maximal area and minimal perimeter.

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