  We study the breaking of parity symmetry in the 2+1 Gross-Neveu model at
finite temperature with chemical potential $\mu$, in the presence of an
external magnetic field. We find that the requirement of gauge invariance,
which is considered mandatory in the presence of gauge fields, breaks parity at
any finite temperature and provides for dynamical mass generation, preventing
symmetry restoration for any non-vanishing $\mu$. The dynamical mass becomes
negligibly small as temperature is raised. We comment on the relevance of our
observation for the gap generation of nodal quasi-particles in the pseudo-gap
phase of high $T_c$ superconductors.
