Applicability of the Linear delta Expansion for the lambda phi**4 Field Theory at Finite Temperature in the Symmetric and Broken Phases

The thermodynamics of a scalar field with a quartic interaction is studied within the linear {delta} expansion (LDE) method. Using the imaginary-time formalism the free energy is evaluated up to second order in the LDE. The method generates nonperturbative results that are then used to obtain thermodynamic quantities like the pressure. The phase transition pattern of the model is fully studied, from the broken to the symmetry restored phase. The results are compared with those obtained with other nonperturbative methods and also with ordinary perturbation theory. The results coming from the two main optimization procedures used in conjunction with the LDE method, the principle of minimal sensitivity (PMS) and the fastest apparent convergence (FAC) are also compared with each other and studied in which cases they are applicable or not. The optimization procedures are applied directly to the free energy.