  Inspired by the bridge pioneered by Guerra among statistical mechanics on
lattice and analytical mechanics on 1+1 continuous Euclidean space-time, we
built a self-consistent method to solve for the thermodynamics of mean-field
models defined on lattice, whose order parameters self average. We show the
whole procedure by analyzing in full details the simplest test case, namely the
Curie-Weiss model. Further we report some applications also to models whose
order parameters do not self-average, by using the Sherrington-Kirkpatrick spin
glass as a guide.
