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

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

1999-08-04

arxiv.org/abs/cond-mat/9908068v1

J.Phys.A32:7249-7261,1999

Physics

Condensed Matter

Statistical Mechanics

16 pages, REVTeX, to be published in J.Phys.A:Math.Gen

Scientific paper

10.1088/0305-4470/32/42/302

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.

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