Chiral symmetry at finite temperature: Linear versus nonlinear sigma models

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 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 f(pi) and the scalar condensate at low temperatures in both models, showing that they are independent of field redefinition.