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We show that the exact beta-function \beta(g) in the continuous 2D g\Phi^{4}model possesses the Kramers-Wannier duality symmetry. The duality symmetrytransformation \tilde{g}=d(g) such that \beta(d(g))=d'(g)\beta(g) isconstructed and the approximate values of g^{*} computed from the dualityequation d(g^{*})=g^{*} are shown to agree with the available numericalresults. The calculation of the beta-function \beta(g) for the 2D scalarg\Phi^{4} field theory based on the strong coupling expansion is developed andthe expansion of \beta(g) in powers of g^{-1} is obtained up to order g^{-8}.The numerical values calculated for the renormalized coupling constantg_{+}^{*} are in reasonable good agreement with the best modern estimatesrecently obtained from the high-temperature series expansion and with thoseknown from the perturbative four-loop renormalization-group calculations. Theapplication of Cardy's theorem for calculating the renormalized isothermalcoupling constant g_{c} of the 2D Ising model and the related universalcritical amplitudes is also discussed.Comment: 16 pages, REVTeX, to be published in J.Phys.A:Math.Ge

Duality symmetry, strong-coupling expansion and universal critical amplitudes in two-dimensional Phi4field models

Duality symmetry, strong-coupling expansion and universal critical amplitudes in two-dimensional Phi⁴field models