  Anisotropy effects on the finite-size critical behavior of a two-dimensional
Ising model on a general triangular lattice in an infinite-strip geometry with
periodic, antiperiodic, and free boundary conditions (bc) in the finite
direction are investigated. Exact results are obtained for the scaling
functions of the finite-size contributions to the free energy density. With
xi_> the largest and xi_< the smallest bulk correlation length at a given
temperature near criticality, we find that the dependence of these functions on
the ratio xi_< / xi_> and on the angle parameterizing the orientation of the
correlation volume is of geometric rather than dynamic origin. Since the
scaling functions are independent of the particular microscopic realization of
the anisotropy within the two-dimensional Ising model, our results provide a
limited verification of universality. We explain our observations by
considering finite-size scaling of free energy densities of general weakly
anisotropic 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 shear
transformation relating the anisotropic and isotropic cases. This allows us to
relate free energy scaling functions in the presence of an anisotropy to those
of the corresponding isotropic system. We interpret our results as a simple and
transparent case of anisotropic universality, where, compared to the isotropic
case, scaling functions depend additionally on the shape and orientation of the
correlation volume. We conjecture that this universality extends to cases where
the geometry and/or the bc are not invariant under the shear transformation and
argue in favor of validity of two-scale factor universality for anisotropic
systems.
