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 $N=4$ fermion species is investigated numerically at non-zero temperature T and chemical potential \ensuremath{\mu}. The phase diagram in the $(\ensuremath{\mu},T)$ plane is mapped out quantitatively. A detailed finite size scaling analysis shows that the $T=0,$ $\ensuremath{\mu}\ensuremath{\ne}0$ chiral phase transition is first order, whereas the $T\ensuremath{\ne}0,$ $\ensuremath{\mu}\ensuremath{\ne}0$ 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 $T=0$ provided no evidence for a nuclear liquid-gas transition at $\ensuremath{\mu}l{\ensuremath{\mu}}_{c}.$