Phase structure of generalized Cross-Neveu models

A phase structure of models with n spinor multiplets has been considered in the space-time of dimension D=2,3. In the case when n=2 and D=3 there may occur vaccums | +> violating chiral invariance, as well as |-> violating P,T symmetry of the model. At D,n=2 depending on the sign of the constant g12 there also exist two different vacua. It is shown here, that at sufficiently small g12 the description of the model with the help of the leading order of 1/N expansion is incorrect (there appear tachyons). The properties of Gross-Neveu model have been dealt with at D=3, n=1 and the temperature and chemical potential not equal to zero