Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Metastability for the degenerate Potts Model with negative external magnetic field under Glauber dynamics (2105.14335v4)

Published 29 May 2021 in math.PR

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 negative external magnetic field. In this scenario there are $q-1$ stable configurations and a unique metastable state. We describe the asymptotic behavior of the first hitting time from the metastable to the set of the stable states 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 identify the union of all minimal gates for the transition from the metastable state both to the set of the stable states and to a fixed stable state. Furthermore, we identify the tube of typical trajectories for these two transitions. The accurate knowledge of the energy landscape allows us to give precise asymptotics for the expected transition time from the unique metastable state to the set of the stable configurations.

Summary

We haven't generated a summary for this paper yet.