  We present a novel picture of a non isothermal solidification process
starting from a molecular level, where the microscopic origin of the basic
mechanisms and of the instabilities characterizing the approach to equilibrium
is rendered more apparent than in existing approaches based on coarse grained
free energy functionals \`a la Landau.
  The system is composed by a lattice of Potts spins, which change their state
according to the stochastic dynamics proposed some time ago by Creutz. Such a
method is extended to include the presence of latent heat and thermal
conduction.
  Not only the model agrees with previous continuum treatments, but it allows
to introduce in a consistent fashion the microscopic stochastic fluctuations.
These play an important role in nucleating the growing solid phase in the melt.
The approach is also very satisfactory from the quantitative point of view
since the relevant growth regimes are fully characterized in terms of scaling
exponents.
