  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 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
g\Phi^{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 Cardy's theorem for calculating the renormalized isothermal
coupling constant g_{c} of the 2D Ising model and the related universal
critical amplitudes is also discussed.
