Theoretical and Mathematical Physics

, Volume 190, Issue 3, pp 431–438 | Cite as

Renormalized coupling constants for the three-dimensional scalar λ ϕ 4 field theory and pseudo-ε-expansion

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Abstract

The renormalized coupling constants g 2k that enter the equation of state and determine nonlinear susceptibilities of the system have universal values g 2k * at the Curie point. We use the pseudo-ε-expansion approach to calculate them together with the ratios R 2k = g 2k /g 4 k-1 for the three-dimensional scalar λ ϕ 4 field theory. We derive pseudo-ε-expansions for g 6 * , g 8 * , R 6 * , and R 8 * in the five-loop approximation and present numerical estimates for R 6 * and R 8 * . The higher-order coefficients of the pseudo-ε-expansions for g 6 * and R 6 * are so small that simple Padé approximants turn out to suffice for very good numerical results. Using them gives R 6 * = 1.650, while the recent lattice calculation gave R 6 * = 1.649(2). The pseudo-ε-expansions of g 8 * and R 8 * are less favorable from the numerical standpoint. Nevertheless, Padé–Borel summation of the series for R 8 * gives the estimate R 8 * = 0.890, differing only slightly from the values R 8 * = 0.871 and R 8 * = 0.857 extracted from the results of lattice and field theory calculations.

Keywords

nonlinear susceptibility effective coupling constant Ising model renormalization group pseudo-ε-expansion 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. Petersburg, Staryi PetergofRussia
  2. 2.National Research University ITMOSt. PetersburgRussia

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