  We apply the thermal (imaginary time) perturbative expansion to the relevant
effective field theory to compute characteristics of the phase transition to
the ordered state which can occur at low temperatures in the gas of
(nonrelativistic) spin 1/2 fermions interacting through a short-range spin
independent repulsive binary interaction potential. We show how to obtain a
systematic expansion of the system's free energy depending on the densities
$n_+$ and $n_-$ of spin-up and spin-down fermions. In this paper we truncate
this expansion at the second order and determine, by numerically minimizing the
free energy, the equilibrium proportions of $n_+$ and $n_-$ (that is, the
system's polarization) as functions of the temperature, the system's overall
density $n = n_+ + n_-$ and the strength of the interaction.
