Can Sigma Models Describe Finite Temperature Chiral Transitions?

TL;DR

This paper challenges the applicability of sigma models to finite temperature chiral transitions, showing that in certain models the transition follows mean field theory rather than the expected universality class.

Contribution

It demonstrates that the standard sigma model scenario fails in the 3D Gross-Neveu model due to the absence of canonical scalar fields, with implications for theories like QCD.

Findings

Finite temperature transition in the 3D Gross-Neveu model is mean field.

Standard sigma model scenario does not apply due to lack of canonical scalar fields.

Results may be relevant for theories with dynamical symmetry breaking like QCD.

Abstract

Large-N expansions and computer simulations indicate that the universality class of the finite temperature chiral symmetry restoration transition in the 3D Gross-Neveu model is mean field theory. This is a counterexample to the standard 'sigma model' scenario which predicts the 2D Ising model universality class. We trace the breakdown of the standard scenario (dimensional reduction and universality) to the absence of canonical scalar fields in the model. We point out that our results could be generic for theories with dynamical symmetry breaking, such as Quantum Chromodynamics.