Renormalization group optimized λϕ4 pressure at next-to-next-to-leading order

We investigate the renormalization group optimized perturbation theory (RGOPT) at next-to-next-to-leading order (NNLO) for thermal scalar field theory. From comparing three thus available successive RGOPT orders we illustrate efficient resummation and very good apparent convergence properties of method. In particular remnant scale dependence thermodynamical quantities is drastically improved as compared to both standard perturbative expansions other related methods, such screened Our present results constitute a useful first NNLO illustration in view applications this approach more involved QCD.