Highly Accurate Critical Exponents from Self-Similar Variational Perturbation Theory

Abstract

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 $\vp^4$ theory. From only three-loop perturbation expansions in $4-\epsilon$ dimensions we obtain {\em 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 $\al\approx-0.0127$ 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 $\nu$ and $\gamma =\nu (2-\eta )$ with high precision.

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References in corpus (1)

• Large order asymptotics and convergent perturbation theory for critical indices of the ${\varphi }^4$ model in $4-\epsilon$ expansion