Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory - art. no. 056113

We use variational perturbation theory to calculate various universal ampli tude ratios above and below T-c in minimally subtracted phi (4) theory with N components in three dimensions. In order to best exhibit the method as a powerful alternative to Borel resummation techniques, we consider only two - and three-loops expressions where our results are analytic expressions. F or the critical exponents, we also extend existing analytic expressions for two loops to three loops.