The four-Fermi model in three dimensions at non-zero density and temperature

Abstract

The four-Fermi model with discrete chiral symmetry is studied in three dimensions at non-zero chemical potential and temperature using the hybrid Monte Carlo algorithm. The number of fermion flavors is chosen large ( N f = 12) to compare with analytic results. A first order chiral symmetry restoring transition is found at zero temperature with a critical chemical potential μ c in good agreement with the large N f calculations. The critical index v of the correlation length is measured in good agreement with analytic calculations. The two-dimensional phase diagram (chemical potential vs. temperature) is mapped out quantitatively. Finite size effects on relatively small lattices and non-zero fermion mass effectsare seen to smooth out the chiral transition dramatically.