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.
Funding Statement
F.R.N. was partially supported by the Netherlands Organisation for Scientific Research (NWO) [Gravitation Grant number 024.002.003–NETWORKS]. A.T. has been supported by the H2020 Project Stable and Chaotic Motions in the Planetary Problem (Grant 677793 StableChaoticPlanetM of the European Research Council). V.J. and F.R.N. are grateful to INDAM-GNAMPA.
Acknowledgments
Unfortunately Francesca passed away on 21 October 2021, before the completion of the review process of the manuscript. She kept working passionately on this paper until the end and every page is full of her love for mathematics and for life. Francesca, we miss you.
The Authors are grateful to Cristian Spitoni for valuable suggestions.
Citation
Valentina Apollonio. Vanessa Jacquier. Francesca Romana Nardi. Alessio Troiani. "Metastability for the Ising model on the hexagonal lattice." Electron. J. Probab. 27 1 - 48, 2022. https://doi.org/10.1214/22-EJP763
Information
