A note on the Ising model in high dimensions

The authors consider the /b d/-dimensional Ising model with a nearest neighbor ferromagnetic interaction /b J/(/b d/)=1/4/b d/. They show that as /b d/ rarr infinity the + phase (and the - phase) approaches a product measure with the density given by the mean field approximation. In particular the spontaneous magnetization converges to its mean field value. A similar result holds for the unique Gibbs measure of the system subject to an external field /b h/ ne 0.Anglai