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

Abstract

We show that the exact beta-function β(g) in the continuous 2D gΦ^{4} model possesses the Kramers-Wannier duality symmetry. The duality symmetry transformation \tilde{g}=d(g) such that β(d(g))=d'(g)β(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 β(g) for the 2D scalar gΦ^{4} field theory based on the strong coupling expansion is developed and the expansion of β(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.

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

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• Universal amplitude ratios in the two-dimensional Ising model
• The 2n-point renormalized coupling constants in the 3d Ising model: estimates by high temperature series to order beta^17
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Cited by in corpus (5)

• Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) model
• Renormalization Group Functions of the ϕ^4 Theory in the Strong Coupling Limit: Analytical Results
• Universal Large-order asymptotic behavior of the Strong-coupling and High-Temperature series expansions
• Exact finite-size scaling with corrections in the two-dimensional Ising model with special boundary conditions
• Critical renormalized coupling constants in the symmetric phase of the Ising models