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 . 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 , 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.
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.
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  and for useful comments.
"Metastability for the dilute Curie–Weiss model with Glauber dynamics." Electron. J. Probab. 26 1 - 38, 2021. https://doi.org/10.1214/21-EJP610