Dynamical behavior in the (2+1)-dimensional gross-neveu model with a thirring interaction

Abstract

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 the fermion self-energy function is constructed up to next-to-leading order in the 1/N expansion. We determine the critical surface which is the boundary between a broken phase and an unbroken one in $(α_c, β_c, N_c)$ space. It is observed that the critical behavior is mainly controlled by the Gross-Neveu coupling $α_c$ and the region of the broken phase is separated into two parts by the line $α_c = α_c^*=\frac{8}{π^2}$. The mass function is strongly dependent upon the flavor number N for $\alpha ＞ α_c^*$, while weakly for $α ＜ α_c^*$. For $α_c ＞ α_c^*$, the critical flavor number $N_c$ increases as the Thirring coupling $β_c$ 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 ultraviolet property of the composite operators.