  We study the O(N) linear sigma model with spontaneous symmetry breaking,
using a Hartree-like ansatz with a classical field and variational masses. We
go beyond the Hartree approximation by including the two-loop contribution, the
sunset diagram, using the 2PPI expansion. We have computed numerically the
effective potential at finite temperature. We find a phase transition of second
order, while it is first order in the Hartree approximation. We also discuss
some implications of the fact that in this order, the decay of the sigma into
two pions affects the thermal diagrams.
