Journal of Physical Studies 1(3), 362–365 (1997) DOI: https://doi.org/10.30970/jps.01.362 ON FREE ENERGY OF THREE-DIMENSIONAL ISING MODEL AT CRITICALITY

A. I. Sokolov, V. A. Ul'kov, E. V. Orlov
Department of Physical Electronics, State Electrotechnical University,
5 Prof. Popov Str., St.Petersburg 197376, Russia

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 $g_6$ and eight-point $g_8$ effective coupling constants are calculated in the three-loop approximation. Their numerical values, universal at criticality, are estimated by means of the Padé and Padé-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 $g_6^*$ 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 $g_6^*$ are shown to be in a good agreement with each other, differing considerably from the values given by other methods.

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