  A complete thermodynamical analysis of the 2+1 dimensional massless
Gross-Neveu model is performed using the optimized perturbation theory. This is
a non-perturbative method that allows us to go beyond the known large-N results
already at lowest order. Our results, for a finite number of fermion species,
N, show the existence of a tricritical point in the temperature and chemical
potential phase diagram for discrete chiral phase transition allowing us to
precisely to locate it. By studying the phase diagram in the pressure and
inverse density plane, we also show the existence of a liquid-gas phase, which,
so far, was unknown to exist in this model. Finally, we also derive N dependent
analytical expressions for the fermionic mass, critical temperature and
critical chemical potential.
