Optimized perturbation theory at finite temperature -: Two-loop analysis

We study the optimized perturbation theory (OPT) at finite temperature, which is a self-consistent resummation method. Firstly, we generalize the idea of the OPT to optimize the coupling constant in lambda phi (4) theory, and give a proof of the renormalizability of this generalized OPT. Secondly, the principle of minimal sensitivity and the criterion of the fastest apparent convergence, which are conditions to determine the optimal parameter values, are examined in lambda phi (4) theory. Both conditions exhibit a second-order transition at finite temperature with critical exponent beta = 0.5 in the two-loop approximation.