Computation of $\beta(g_c)$ at O(1/N^2) in the O(N) Gross Neveu Model in Arbitrary Dimensions

TL;DR

This paper calculates the critical exponent of the beta function at order 1/N^2 in the O(N) Gross Neveu model across arbitrary dimensions using advanced field-theoretic techniques.

Contribution

It provides a novel computation of the beta function's critical exponent at O(1/N^2) in the Gross Neveu model for any dimension, extending previous results.

Findings

Critical exponent of the beta function at O(1/N^2) derived

Method involves corrections to asymptotic scaling forms and Schwinger Dyson equations

Results applicable to arbitrary dimensions

Abstract

By using the corrections to the asymptotic scaling forms of the fields of the $O(N)$ Gross Neveu model to solve the dressed skeleton Schwinger Dyson equations, we deduce the critical exponent corresponding to the $\beta$-function of the model at $O(1/N^2)$.