We study the O(N ) linear sigma model with spontaneous symmetry breaking at finite temperature in the framework of the two-particle point-irreducible (2PPI) effective action. We go beyond the Hartree approximation by including the twoloop contribution, i.e., the sunset diagram. A phase transition of second order is found, whereas it is of first order in the one-loop Hartree approximation. Furthermore, we show the temperature-dependence of the variational mass parameters and comment on their relation to the physical sigma and pion masses. * talk given by S. Michalski.

We consider the out-of-equilibrium evolution of a classical condensate field and its quantum fluctuations for a scalar O(N) model with spontaneously broken symmetry. In contrast to previous studies we do not consider the large N limit, but the case of finite N , including N = 1, i.e., plain λφ 4 theory. The instabilities encountered in the one-loop approximation are prevented, as in the large-N limit, by back reaction of the fluctuations on themselves, or, equivalently, by including a resummation of bubble diagrams. For this resummation and its renormalization we use formulations developed recently based on the effective action formalism of Cornwall, Jackiw and Tomboulis. The formulation of renormalized equations for finite N derived here represents a useful tool for simulations with realistic models. Here we concentrate on the phase structure of such models. We observe the transition between the spontaneously broken and the symmetric phase at low and high energy densities, respectively. This shows that the typical structures expected in thermal equilibrium are encountered in nonequilibrium dynamics even at early times, i.e., before an efficient rescattering can lead to thermalization.