  The 2+1d Gross-Neveu model with finite density and finite temperature are
studied by the staggered fermion discretization. The kinetic part of this
staggered fermion in momentum space is used to build the relation between the
staggered fermion and Wilson-like fermion. In the large Nf limit (the number Nf
of staggered fermion flavors), the chiral condensate and fermion density are
solved from the gap equation in momentum space, and thus the phase diagram of
fermion coupling, temperature and chemical potential are obtained. Moreover, an
analytic formula for the inverse of the staggered fermion matrix are given
explicitly, which can be calculated easily by parallelization. The
generalization to the 1+1d and 3+1d cases are also considered.
