Highly Accurate Critical Exponents from Self-Similar Variational Perturbation Theory

2004/02/05 by H. Kleinert, V. I. Yukalov
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.71.026131

published as Phys.Rev. E71 (2005) 026131 · Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/kleiner_re349/preprint.html

arxiv created 2004/02/05 · arxiv updated 2009/12/01

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 \vp⁴ theory. From only three-loop perturbation expansions in 4- ε 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≈-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.

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