Dimensional reduction of the chiral-continous Gross-Neveu model

TL;DR

This paper investigates the finite-temperature phase transition of the generalized Gross-Neveu model with continuous chiral symmetry, deriving a dimensionally reduced theory and analyzing symmetry restoration and universality class.

Contribution

It introduces a dimensionally reduced theory for the model at finite temperature and analyzes symmetry restoration and critical behavior using the $1/N$ expansion.

Findings

Finite-temperature induces a discrete degeneracy in the vacuum.

Symmetry can be partially or totally restored depending on parameters.

The universality class of the reduced theory is identified.

Abstract

We study the finite-temperature phase transition of the generalized Gross-Neveu model with continous chiral symmetry in $2 < d \leq 4$ euclidean dimensions. The critical exponents are computed to the leading order in the $1/N$ expansion at both zero and finite temperatures. A dimensionally reduced theory is obtained after the introduction of thermal counterterms necessary to cancel thermal divergences that arise in the limit of high temperature. Although at zero temperature we have an infinitely and continously degenerate vacuum state, we show that at finite temperature this degeneracy is discrete and, depending on the values of the bare parameters, we may have either total or partial restoration of symmetry. Finally we determine the universality class of the reduced theory by a simple analysis of the infrared structure of thermodynamic quantities computed using the reduced action as starting point.