Self-similar variational perturbation theory for critical exponents

We extend field theoretic variational perturbation theory by self-similar approximation theory, which greatly accelerates convergence. This is illustrated by recalculating the critical exponents of O (N) -symmetric phi(4) theory. From only three-loop perturbation expansions in 4-epsilon dimensions, we obtain analytic results for the exponents, which are close to those derived recently from ordinary field-theoretic variational perturbational theory to seventh order. In particular, the specific-heat exponent is found to be in good agreement with best-measured exponent alpha approximately -0.0127 of the specific-heat peak in superfluid helium, found in a satellite experiment. In addition, our analytic expressions reproduce also the exactly known large- N behavior of the exponents.