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On the Symmetry of Universal Finite-Size Scaling Functions in Anisotropic Systems

Alfred Hucht
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Abstract

In this work a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation is postulated. This transformation connects the properties of a finite two-dimensional system at criticality with generalized aspect ratio $ρ> 1$ to a system with $ρ< 1$. The symmetry is formulated within a finite-size scaling theory, and expressions for several universal amplitude ratios are derived. The predictions are confirmed within the exactly solvable weakly anisotropic two-dimensional Ising model and are checked within the two-dimensional dipolar in-plane Ising model using Monte Carlo simulations. This model shows a strongly anisotropic phase transition with different correlation length exponents $ν_{||} \neq ν_\perp$ parallel and perpendicular to the spin axis.

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Alfred Hucht. 2002-02-08. On the Symmetry of Universal Finite-Size Scaling Functions in Anisotropic Systems. https://doi.org/10.1088/0305-4470%2F35%2F31%2F103

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