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