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- Title
Critical exponents and the pseudo- є-expansion.
- Authors
Nikitina, M.; Sokolov, A.
- Abstract
We present the pseudo- є-expansions ( τ-series) for the critical exponents of a λϕ-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.
- Subjects
PERTURBATION theory; SUPERFLUIDITY; FIELD theory (Physics); HAMILTONIAN operator; FERROMAGNETIC materials
- Publication
Theoretical & Mathematical Physics, 2016, Vol 186, Issue 2, p192
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1134/S0040577916020057