  The massive Gross-Neveu model is solved in the large N limit at finite
temperature and chemical potential. The scalar potential is given in terms of
Jacobi elliptic functions. It contains three parameters which are determined by
transcendental equations. Self-consistency of the scalar potential is proved.
The phase diagram for non-zero bare quark mass is found to contain a
kink-antikink crystal phase as well as a massive fermion gas phase featuring a
cross-over from light to heavy effective fermion mass. For zero bare quark mass
we recover the three known phases kink-antikink crystal, massless fermion gas,
and massive fermion gas. All phase transitions are shown to be of second order.
Equations for the phase boundaries are given and solved numerically.
Implications on condensed matter physics are indicated where our results
generalize the bipolaron lattice in non-degenerate conducting polymers to
finite temperature.
