  Aim of this work is not trying to explore a macroscopic behavior of some
recent model in statistical mechanics but showing how some recent techniques
developed within the framework of spin glasses do work on simpler model,
focusing on the method and not on the analyzed system. To fulfil our will the
candidate model turns out to be the paradigmatic mean field Ising model. The
model is introduced and investigated with the interpolation techniques. We show
the existence of the thermodynamic limit, bounds for the free energy density,
the explicit expression for the free energy with its suitable expansion via the
order parameter, the self-consistency relation, the phase transition, the
critical behavior and the self-averaging properties. At the end a bridge to a
Parisi-like theory is tried and discussed.
