Estimate of the Critical Exponents from the Field-Theoretical Renormalization Group: Mathematical Sense of the "Standard Values"

Details Estimate of the Critical Exponents from the Field-Theoretical Renormalization Group: Mathematical Sense of the "Standard Values" Estimate of the Critical Exponents from the Field-Theoretical Renormalization Group: Mathematical Sense of the "Standard Values"

2010-10-17

arxiv.org/abs/1010.3389v1

J.Exp.Theor.Phys.106:1118,2008; Zh.Eksp.Teor.Fiz.133:1277,2008

Physics

Condensed Matter

Statistical Mechanics

PDF, 12 pages

Scientific paper

10.1134/S1063776108060113

New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and Zinn-Justin (the so-called "standard values"), but have lower uncertainty. It has been shown that usual field-theoretical estimates implicitly imply the smoothness of the coefficient functions. The last assumption is open for discussion in view of the existence of the oscillating contribution to the coefficient functions. The appropriate interpretation of the last contribution is necessary both for the estimation of the systematic errors in the "standard values" and for a further increase in accuracy.

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