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 λφ4 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 λφ4 theory. Both conditions exhibit a second-order transition at finite temperature with critical exponent β=0.5 in the two-loop approximation.