1998/03/28 by A. I. Sokolov, V. A. Ul'kov, E. V. Orlov · 1 citation
Physics and Astronomy · #cond-mat.stat-mech #hep-lat #hep-ph #hep-th
published as J. Phys. Studies 1 (1997) 362-365 · 7 pages, TeX, no figures
arxiv created 1998/03/28 · arxiv updated 2009/11/30
Higher-order vertices at zero external momenta for the scalar field theory describing the critical behaviour of the Ising model are studied within the field-theoretical renormalization group (RG) approach in three dimensions. Dimensionless six-point g6 and eight-point g8 effective coupling constants are calculated in the three-loop approximation. Their numerical values, universal at criticality, are estimated by means of the Pade and Pade-Borel summation of the RG expansions found and by putting the renormalized quartic coupling constant equal to its universal fixed-point value known from six-loop RG calculations. The values of g6^* obtained are compared with their analogs resulting from the ε-expansion, Monte Carlo simulations, the Wegner--Houghton equations and the linked cluster expansion series. The field-theoretical estimates for g6^* are shown to be in a good agreement with each other, differing considerably from the values given by other methods.