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Theoretical and Mathematical Physics

, Volume 186, Issue 2, pp 192–204 | Cite as

Critical exponents and the pseudo-є-expansion

  • M. A. Nikitina
  • A. I. Sokolov
Article

Abstract

We present the pseudo-є-expansions (τ-series) for the critical exponents of a λϕ 4-type three-dimensional O(n)-symmetric model obtained on the basis of six-loop renormalization-group expansions. We present numerical results in the physically interesting cases n = 1, n = 2, n = 3, and n = 0 and also for 4 ≤ n ≤ 32 to clarify the general properties of the obtained series. The pseudo-є-expansions or the exponents γ and α have coefficients that are small in absolute value and decrease rapidly, and direct summation of the τ -series therefore yields quite acceptable numerical estimates, while applying the Padé approximants allows obtaining high-precision results. In contrast, the coefficients of the pseudo-є-expansion of the scaling correction exponent ω do not exhibit any tendency to decrease at physical values of n. But the corresponding series are sign-alternating, and to obtain reliable numerical estimates, it also suffices to use simple Padé approximants in this case. The pseudo-є-expansion technique can therefore be regarded as a distinctive resummation method converting divergent renormalization-group series into expansions that are computationally convenient.

Keywords

three-dimensional O(n)-symmetric model critical exponent pseudo-є-expansion Pad´e approximant numerical result 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.St. Petersburg State UniversityFock Research Institute of PhysicsSt. PetersburgRussia
  2. 2.St. Petersburg National Research University for Information Technologies, Mechanics, and OpticsSt. PetersburgRussia

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