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2021 Metastability for the dilute Curie–Weiss model with Glauber dynamics
Anton Bovier, Saeda Marello, Elena Pulvirenti
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Electron. J. Probab. 26: 1-38 (2021). DOI: 10.1214/21-EJP610

Abstract

We analyse the metastable behaviour of the dilute Curie–Weiss model subject to a Glauber dynamics. The model is a random version of a mean-field Ising model, where the coupling coefficients are Bernoulli random variables with mean p(0,1). This model can be also viewed as an Ising model on the Erdős–Rényi random graph with edge probability p. The system is a Markov chain where spins flip according to a Metropolis dynamics at inverse temperature β. We compute the average time the system takes to reach the stable phase when it starts from a certain probability distribution on the metastable state (called the last-exit biased distribution), in the regime where N, β>βc=1 and h is positive and small enough. We obtain asymptotic bounds on the probability of the event that the mean metastable hitting time is approximated by that of the Curie–Weiss model. The proof uses the potential theoretic approach to metastability and concentration of measure inequalities.

Funding Statement

This work was partly funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – GZ 2047/1, Projekt-ID 390685813 and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Projektnummer 211504053 – SFB 1060.

Acknowledgments

We thank Alessandra Bianchi for fruitful discussions on capacity estimates and Frank den Hollander for giving us early access to his article in preparation with Oliver Jovanovski [11] and for useful comments.

Citation

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Anton Bovier. Saeda Marello. Elena Pulvirenti. "Metastability for the dilute Curie–Weiss model with Glauber dynamics." Electron. J. Probab. 26 1 - 38, 2021. https://doi.org/10.1214/21-EJP610

Information

Received: 20 January 2020; Accepted: 29 March 2021; Published: 2021
First available in Project Euclid: 20 April 2021

arXiv: 1912.10699
Digital Object Identifier: 10.1214/21-EJP610

Subjects:
Primary: 60K35, 60K37, 82B20, 82B44

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