Chiral symmetry at finite temperature: linear vs nonlinear $\sigma$-models

Abstract

The linear O($N$) sigma model undergoes a symmetry restoring phase transition at finite temperature. We show that the nonlinear O($N$) sigma model also undergoes a symmetry restoring phase transition; the critical temperatures are the same when the linear model is treated in mean field approximation and the nonlinear model is treated to leading plus subleading order in the 1/$N$ expansion. We also carefully define and study the behavior of $f_{\pi }$ and the scalar condensate at low temperatures in both models, showing that they are independent of field redefinition.

arXiv comment29 pages, regular Latex, 5 figures in one Postscript file

References in corpus (7)

• Static and Dynamic Critical Phenomena at a Second Order QCD Phase Transition
• Emergence of Coherent Long Wavelength Oscillations After a Quench: Application to QCD
• Weinberg-Type Sum Rules at Zero and Finite Temperature
• Scaling of Pseudo-Critical Couplings in Two-Flavour QCD
• Can Sigma Models Describe Finite Temperature Chiral Transitions?
• Spatial and Temporal Hadron Correlators below and above the Chiral Phase Transition
• The Goldberger -- Treiman Relation, $g_A$ and $g_{\pi NN}$ at $T\ne 0$

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