The Dynamical Behaviors in (2+1)-Dimensional Gross-Neveu Model with a Thirring Interaction

We analyze (2+1)-dimensional Gross-Neveu model with a Thirring interaction, where a vector-vector type four-fermi interaction is on equal terms with a scalar-scalar type one. The Dyson-Schwinger equation for fermion self-energy function is constructed up to next-to-leading order in 1/N expansion. We determine the critical surface which is the boundary between a broken phase and an unbroken one in (αc, βc, Nc) space. It is observed that the critical behavior is mainly controlled by Gross-Neveu coupling αc and the region of the broken phase is separated into two parts by the line αc = α ∗ c(= 8 π ). The mass function is strongly dependent upon the flavor e-mail: [email protected] e-mail: [email protected] 1 number N for α > α∗ c , while weakly for α < α ∗ c . For α > α ∗ c , the critical flavor number Nc increases as Thirring coupling β decreases. By driving the CJT effective potential, we show that the broken phase is energetically preferred to the symmetric one. We discuss the gauge dependence of the mass function and the ultra-violet property of the composite operators.