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We explain the Curie Weiss model in Statistical Mechanics within the Ergodicviewpoint. More precisely, we simultaneously define in$\{-1,+1\}^{\mathbb{N}}$, on the one hand a generalized Curie Weiss modelwithin the Statistical Mechanics viewpoint and on the other hand, quadraticfree energy and quadratic pressure within the Ergodic Theory viewpoint. We showthat there are finitely many invariant measures which maximize the quadraticfree energy. They are all Dynamical Gibbs Measures. Moreover, the ProbabilisticGibbs measures for generalized Curie Weiss model converge to a determinedcombination of the (dynamical) conformal measures associated to these DynamicalGibbs Measures. The standard Curie Weiss model is a particular case of ourgeneralized Curie Weiss model. An Ergodic viewpoint over the Curie Weiss Pottsmodel is also given.

Generalized Curie-Weiss Model and Quadratic Pressure in Ergodic Theory