O(N) linear and nonlinear sigma model at T ≠0 with the auxiliary field method

A study of the linear and nonlinear versions of the O(N) model is presented at nonzero temperature. We apply the auxiliary field method to compute the chiral condensate, the pion mass, the σ mass and the pressure as functions of temperature by using the CJT formalism. A careful treatment of the limiting process of the coefficient of the auxiliary field allows us to establish a well defined link between the linear and nonlinear form of the model. In the region where the parameter space of the model allows for solutions of the gap equations, Goldstone's theorem is always fulfilled. In the linear version of the model with explicitly broken chiral symmetry the order of the phase transition depends on the vacuum mass of the σ particle. However, in the nonlinear case and in the large-N limit, the order of the phase transition coincides with predictions of universality class arguments.