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

The Staggered Fermion for the Gross-Neveu Model at Non-zero Temperature and Density