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

TL;DR

This paper investigates the phase structure and critical behavior of a (2+1)-dimensional Gross-Neveu model with Thirring interaction, analyzing how coupling constants and flavor number influence symmetry breaking and phase transitions.

Contribution

It provides a detailed analysis of the critical surface and phase boundary in the model, incorporating next-to-leading order Dyson-Schwinger equations and exploring the effects of Thirring coupling.

Findings

Critical surface determined in parameter space.

Broken phase region separated by a specific coupling line.

Mass function strongly depends on flavor number for certain couplings.

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 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 ($\alpha_c,~ \beta_c,~ N_c$) space. It is observed that the critical behavior is mainly controlled by Gross-Neveu coupling $\alpha_c$ and the region of the broken phase is separated into two parts by the line $\alpha_c=\alpha_c^*(=\frac{8}{\pi^2})$. The mass function is strongly dependent upon the flavor number N for $\alpha > \alpha_c^*$, while weakly for $\alpha < \alpha_c^*$. For $\alpha > \alpha_c^*$, the critical flavor number $N_c$ increases as Thirring coupling $\beta$ 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.