Thermodynamics of the O(4) linear and nonlinear models within the auxiliary field method

The study of the O(N) model at nonzero temperature is presented applying the auxiliary field method, which allows to obtain a continuous transformation between the linear and the nonlinear version of the model. In case of explicitly broken chiral symmetry the order of the chiral phase transition changes from crossover to first order as the vacuum mass of the $\sigma$ particle increases. In the chiral limit one observes a first order phase transition and the Goldstone’s theorem is fulfilled.