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Anisotropy effects on the finite-size critical behavior of a two-dimensionalIsing model on a general triangular lattice in an infinite-strip geometry withperiodic, antiperiodic, and free boundary conditions (bc) in the finitedirection are investigated. Exact results are obtained for the scalingfunctions of the finite-size contributions to the free energy density. Withxi_> the largest and xi_< the smallest bulk correlation length at a giventemperature near criticality, we find that the dependence of these functions onthe ratio xi_< / xi_> and on the angle parameterizing the orientation of thecorrelation volume is of geometric rather than dynamic origin. Since thescaling functions are independent of the particular microscopic realization ofthe anisotropy within the two-dimensional Ising model, our results provide alimited verification of universality. We explain our observations byconsidering finite-size scaling of free energy densities of general weaklyanisotropic models on a d-dimensional film, i.e., in an L x infinity^(d-1)geometry, with bc in the finite direction that are invariant under a sheartransformation relating the anisotropic and isotropic cases. This allows us torelate free energy scaling functions in the presence of an anisotropy to thoseof the corresponding isotropic system. We interpret our results as a simple andtransparent case of anisotropic universality, where, compared to the isotropiccase, scaling functions depend additionally on the shape and orientation of thecorrelation volume. We conjecture that this universality extends to cases wherethe geometry and/or the bc are not invariant under the shear transformation andargue in favor of validity of two-scale factor universality for anisotropicsystems.

Universal anisotropic finite-size critical behavior of the two-dimensional Ising model on a strip and of d-dimensional models on films