Abstract:
The Curie-Weiss model (CW) is a classical model of a ferromagnetic spin
system in which all spins interact with each other, namely the interaction
graph is complete.
The randomly dilute Curie-Weiss model (RDCW) is a generalisation of the CW
in which the deterministic interaction between pairs of spins is replaced by
iid random coefficients. It can be also viewed as an Ising model on a random
graph. We will show results in the case where the interaction coefficients
are iid Bernoulli random variables with fixed parameter p, i.e. the
interaction graph is an Erdős–Rényi random graph.
After giving an introduction on metastability and on the well known results
for the CW, we will focus on how the mean metastable hitting time in the
RDCW can be approximated by that of the CW, asymptotically as the system
size grows. The main methods we used are potential theoretic approach to
metastability and concentration of measure inequalities.
Based on joint work with Anton Bovier and Elena Pulvirenti.