  We study the O(N) symmetric linear sigma model at finite temperature as the
low-energy effective models of quantum chromodynamics(QCD) using the
Cornwall-Jackiw-Tomboulis(CJT) effective action for composite operators. It has
so far been claimed that the Nambu-Goldstone theorem is not satisfied at finite
temperature in this framework unless the large N limit in the O(N) symmetry is
taken. We show that this is not the case. The pion is always massless below the
critical temperature, if one determines the propagator within the form such
that the symmetry of the system is conserved, and defines the pion mass as the
curvature of the effective potential. We use a new renormalization prescription
for the CJT effective potential in the Hartree-Fock approximation. A numerical
study of the Schwinger-Dyson equation and the gap equation is carried out
including the thermal and quantum loops. We point out a problem in the
derivation of the sigma meson mass without quantum correction at finite
temperature. A problem about the order of the phase transition in this approach
is also discussed.

High Energy Physics - Phenomenology