Can Sigma Models Describe Finite Temperature Chiral Transitions?

Details Can Sigma Models Describe Finite Temperature Chiral Transitions? Can Sigma Models Describe Finite Temperature Chiral Transitions?

1994-07-27

arxiv.org/abs/hep-lat/9407021v1

Phys.Rev.Lett. 74 (1995) 3109-3112

Physics

High Energy Physics

High Energy Physics - Lattice

9 pages, 2 ps figures

Scientific paper

10.1103/PhysRevLett.74.3109

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.

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