Metastability for dilute spin models with Glauber dynamics

Pulvirenti Elena, TU Delft

I will first introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model and the Potts model on inhomogeneous dense random graphs. I will then present quantitative estimates of metastability in large volumes at fixed temperatures when these systems evolve according to a Glauber dynamics, i.e. where spins flip with Metropolis rates at inverse temperature β. The main result identifies conditions ensuring that with high probability the system behaves like the corresponding system where the random couplings are replaced by their averages. More precisely, we prove that the metastability of the former system is implied with high probability by the metastability of the latter. Moreover, we consider relevant metastable hitting times of the two systems and find the asymptotic tail behaviour and the moments of their ratio. Our proofs use the potential-theoretic approach to metastability in combination with concentration inequalities. Based on joint works in collaboration with Anton Bovier, Johan Dubbeldam, Frank den Hollander, Vicente Lenz, Saeda Marello, Martin Slowik.

Area: IS5 - Metastability (Elena Pulvirenti)

Keywords: mean-field spin systems, Ising model, metastable hitting times