Duality symmetry, strong coupling expansion and universal critical amplitudes in two-dimensional \Phi^{4} field models

TL;DR

This paper demonstrates the duality symmetry of the beta-function in the 2D ^4 field model, develops a strong coupling expansion, and discusses universal critical amplitudes, aligning theoretical results with numerical and perturbative data.

Contribution

It introduces the exact duality symmetry of the beta-function in the 2D ^4 model and computes the beta-function using a strong coupling expansion up to order g^{-8}.

Findings

Duality symmetry of the beta-function is established and verified.

Strong coupling expansion of eta(g) matches numerical estimates.

Universal critical amplitudes are discussed in relation to the 2D Ising model.

Abstract

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.