Nontrivial topology, finite particle density, and chiral symmetry in the Gross-Neveu model

The phase structure of the Gross-Neveu model with chemical potential mu is studied in spacetime with R(1) x S-1 topology. In the (mu lambda) = 1/L plane (where L is the length of the circle S-1), the phase portraits of the model are constructed for periodic and antiperiodic boundary conditions. For the first time, it is shown that at least three phases-one massless phase and two massive phases with spontaneously broken chiral symmetry-exist in both cases and that there is one tricritical point at which these phases are in contact. Equations are found for the phase boundaries, the critical curves of first- and second-order phase transitions.