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

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 $\rho >1$ to a system with $\rho <1$. 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 ${\nu }_{||}\ne {\nu }_{\perp }$ parallel and perpendicular to the spin axis.

RevTeX4, 4 pages, 3 figures

References in corpus (2)

• Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle
• Anisotropic scaling and generalized conformal invariance at Lifshitz points

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