The Critical Exponents Of The Matrix Valued Gross-Neveu Model

TL;DR

This paper investigates the critical behavior of the matrix-valued Gross-Neveu model in dimensions between 2 and 4, deriving approximate critical exponents and validating the method on vector models.

Contribution

It introduces a combined approximation method to analyze the large N limit of the matrix Gross-Neveu model and computes its critical exponents.

Findings

The model exhibits a phase transition at finite critical temperature.

Approximate critical exponents are nu = 1/(2(d-2)) and eta = d-2.

The approximation method yields exact leading-order results for vector models.

Abstract

We study the large N limit of the MATRIX valued Gross-Neveu model in 2<d<4 dimensions. The method employed is a combination of the approximate recursion formula of Polyakov and Wilson with the solution to the zero dimensional large N counting problem of Makeenko and Zarembo. The model is found to have a phase transition at a finite value for the critical temperature and the critical exponents are approximated by nu = 1/(2(d-2)) and eta=d-2. We test the validity of the approximation by applying it to the usual vector models where it is found to yield exact results to leading order in 1/N.