Phase transition and critical behaviour of the d=3 Gross-Neveu model

TL;DR

This paper investigates the second order phase transition in the three-dimensional Gross-Neveu model with one fermion species, identifying its universality class and calculating critical exponents using exact renormalization group equations.

Contribution

It establishes the existence of a second order phase transition in the d=3 Gross-Neveu model and computes its critical exponents for various fermion numbers using a novel RG approach.

Findings

Identifies a second order phase transition for N=1

Calculates critical exponents: =0.63, =0.31, =0.11

Determines the universality class of the transition

Abstract

A second order phase transition for the three dimensional Gross-Neveu model is established for one fermion species N=1. This transition breaks a paritylike discrete symmetry. It constitutes its peculiar universality class with critical exponent \nu = 0.63 and scalar and fermionic anomalous dimension \eta_\sigma = 0.31 and \eta_\psi = 0.11, respectively. We also compute critical exponents for other N. Our results are based on exact renormalization group equations.