Magnetisation probabilities and metastability in the Ising model

Abstract

Let P(m) be the equilibrium probability that a two-dimensional Ising model with nearest-neighbour interactions on an N*N lattice be found to have magnetisation m. The author calculates P(m) for Tc and find it to agree with certain expectations. Difficulties in the use of P(m) for interpretation of metastability for a system in an external field are stressed. -log P(m) is used as a potential in a Fokker-Planck equation for the diffusion of m under stochastic dynamics and, to the extent that that equation describes the physical system, a formula is derived for the lifetime of metastable states.