RENORMALIZED COUPLING CONSTANTS FOR THE THREE-DIMENSIONAL SCALAR λφ4 FIELD THEORY AND PSEUDO-ε-EXPANSION

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-epsilon-expansion approach to calculate them together with the ratios R-2k = g(2k) /g(4)(k-1) for the three-dimensional scalar lambda phi(4) field theory. We derive pseudo-epsilon-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-epsilon-expansions for g(6)(*) and R-6(*) are so small that simple Pad, 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-epsilon-expansions of g(8)(*) and R-8(*) are less favorable from the numerical standpoint. Nevertheless,Pade-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.