## Abstract

We consider the*d*-dimensional Ising model with a nearest neighbor ferromagnetic interaction*J*(*d*)=1/4*d*. We show that as*d*→∞ the+phase (and the — phase) approaches a product measure with 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*h*≠0.

## Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics High Dimension
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