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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 allow

Author

Kastening, Boris

Published

2012

Language

EN