Chiral symmetry restoration in the three-dimensional four-fermion model at nonzero temperature and density

The three-dimensional four-fermion model with a $Z_2$ chiral symmetry and $N=4\mathrm{}$ fermion species is investigated numerically at non-zero temperature T and chemical potential μ. The phase diagram in the $(\mu ,T)$ plane is mapped out quantitatively. A detailed finite size scaling analysis shows that the $T=0,$ $\mu \ne 0$ chiral phase transition is first order, whereas the $T\ne 0,$ $\mu \ne 0$ transition remains second order down to very low T. Quantitative results for the location of the end of the first order line are given. The simulations at $T=0\mathrm{}$ provided no evidence for a nuclear liquid-gas transition at $\mu <{\mu }_c.$