Magnetisation probabilities and metastability in the Ising model

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 T<T c 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.