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

Alexander Bochkarev·Joseph Kapusta
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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 $f_π$ and the scalar condensate at low temperatures in both models, showing that they are independent of field redefinition.

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Alexander Bochkarev, Joseph Kapusta. 1996-02-27. Chiral symmetry at finite temperature: linear vs nonlinear $σ$-models. https://doi.org/10.1103/physrevd.54.4066

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