Chiral symmetry at finite temperature: Linear versus nonlinear σ models

The linear O(N) σ model undergoes a symmetry-restoring phase transition at finite temperature. We show that the nonlinear O(N) σ model also undergoes a symmetry-restoring phase transition; the critical temperatures are the same when the linear model is treated in the 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 fπ and the scalar condensate at low temperatures in both models, showing that they are independent of field redefinition. copyright 1996 The American Physical Society