Critical exponents and the pseudo-є-expansion

• Published in: Theoretical and mathematical physics 2016-02, Vol.186 (2), p.192-204
• Main Authors: Nikitina, M. A., Sokolov, A. I.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Approximants; Exponents; Mathematical and Computational Physics; Mathematical models; Physics; Physics and Astronomy; Theoretical; Thermal expansion; Three dimensional models
• ISSN: 0040-5779; 1573-9333
• DOI: 10.1134/S0040577916020057

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.