Résumé
Phys.Rev.C81:065205,2010 The optimized perturbation theory (OPT) method is applied to the$SU(2)$version of the Nambu--Jona-Lasinio (NJL) model both at zero and at finite temperature and/or density. At the first nontrivial order the OPT exhibits a class of 1/N_c corrections which produce nonperturbative results that go beyond the standard large-N_c, or mean-field approximation. The consistency of the OPT method with the Goldstone theorem at this order is established, and appropriate OPT values of the basic NJL (vacuum) parameters are obtained by matching the pion mass and decay constant consistently. Deviations from standard large-N_c relations induced by OPT at this order are derived, for example, for the Gell--Mann-Oakes-Renner relation. Next, the results for the critical quantities and the phase diagram of the model, as well as a number of other thermodynamical quantities of interest, are obtained with OPT and then contrasted with the corresponding results at large N_c.