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

• Published in: Theoretical and mathematical physics 2017-03, Vol.190 (3), p.431-438
• Main Authors: Nikitina, M. A., Sokolov, A. I.
• Format: Article
• Language: English
• Subjects: Approximants; Constants; Coupling; Curie temperature; Field theory; Magnetic fields; Thermal expansion
• ISSN: 0040-5779; 1573-9333
• DOI: 10.1134/S0040577917030126

The renormalized coupling constants g2k 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 R2k = g2k/g 4 k-1 for the three-dimensional scalar λϕ4 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.