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

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

2000-09-13

arxiv.org/abs/hep-th/9509068v1

Phys.Rev. D52 (1995) 6109-6115

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, LaTex, 6 ps figure files(uuencoded in seperate file)

Scientific paper

10.1103/PhysRevD.52.6109

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.

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