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Estimate of the critical exponents from the field-theoretical renormalization group: mathematical meaning of the “Standard Values”

  • Order, Disorder, and Phase Transition in Condensed Systems
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Abstract

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 of the standard values and for a further increase in accuracy.

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Authors and Affiliations

  1. Kapitza Institute for Physical Problems, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russia

    A. A. Pogorelov & I. M. Suslov

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  1. A. A. Pogorelov
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  2. I. M. Suslov
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Correspondence to I. M. Suslov.

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Original Russian Text © A.A. Pogorelov, I.M. Suslov, 2008, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 133, No. 6, pp. 1277–1289.

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Pogorelov, A.A., Suslov, I.M. Estimate of the critical exponents from the field-theoretical renormalization group: mathematical meaning of the “Standard Values”. J. Exp. Theor. Phys. 106, 1118–1129 (2008). https://doi.org/10.1134/S1063776108060113

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  • DOI: https://doi.org/10.1134/S1063776108060113

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