We show that the exact beta-function beta(g) in the continuous 2D gPhi^{4} model possesses the Kramers-Wannier duality symmetry. The duality symmetry transformation tilde{g}=d(g) such that beta(d(g))=d(g)beta(g) is constructed and the approximate values of g^{*} computed from the duality equation d(g^{*})=g^{*} are shown to agree with the available numerical results. The calculation of the beta-function beta(g) for the 2D scalar gPhi^{4} field theory based on the strong coupling expansion is developed and the expansion of beta(g) in powers of g^{-1} is obtained up to order g^{-8}. The numerical values calculated for the renormalized coupling constant g_{+}^{*} are in reasonable good agreement with the best modern estimates recently obtained from the high-temperature series expansion and with those known from the perturbative four-loop renormalization-group calculations. The application of Cardys theorem for calculating the renormalized isothermal coupling constant g_{c} of the 2D Ising model and the related universal critical amplitudes is also discussed.
Download