The Phase Structure of the Gross-Neveu Model with Thirring Interaction at the Next to Leading Order of 1/N Expansion

TL;DR

This paper investigates the phase transition behavior of a combined Gross-Neveu and Thirring model in 2<D<4 dimensions using 1/N expansion, revealing a critical surface with a notable change at g=1 and aligning with Schwinger-Dyson results.

Contribution

It provides a gauge invariant effective potential for the model at next-to-leading order and explicitly characterizes the critical surface and phase transition behavior.

Findings

Existence of a chiral phase transition in the model.

Critical surface divided by g=1 with different behaviors.

Results agree with Schwinger-Dyson equation analysis.

Abstract

We study the critical behavior of the D (2<D<4) 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. By using inversion method up to the next-to-leading order of 1/N expansion, we construct a gauge invariant effective potential. We show the existence of the chiral order phase transition, and determine explicitly the critical surface. It is observed that the critical behavior is mainly controlled by the Gross-Neveu coupling g. The critical surface can be divided into two parts by the surface g=1 which is the critical coupling in the Gross-Neveu model at the 1/N next-to-leading order, and the form of the critical surface is drastically change at g=1. Comparison with the Schwinger-Dyson(SD) equation is also discussed. Our result is almost the same as that derived in the SD equation. Especially, in the case of pure Gross-Neveu model, we succeed in deriving exactly the same critical line as the one derived in the SD equation.