Highly Accurate Critical Exponents from Self-Similar Variational Perturbation Theory

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We extend field theoretic variational perturbation theory by self-similar approximation theory, which greatly accelerates convergence. This is illustrated by re-calculating the critical exponents of O(N)-symmetric ⁴ theory. From only three-loop perturbation expansions in 4- ε dimensions we obtain analytic results for the exponents, with practically the same accuracy as those derived recently from ordinary field-theoretic variational perturbational theory to seventh order. In particular, the theory explains the best-measured exponent ≈-0.0127 of the specific heat peak in superfluid helium, found in a satellite experiment with a temperature resolution of nanoKelvin. In addition, our analytic expressions reproduce also the exactly known large-N behaviour of the exponents ν and γ= ν(2- η) with high precision.