Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics
arXiv:2108.04011 · doi:10.1016/j.spa.2024.104343
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 stable configuration and 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.
arXiv commentpg. 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
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