NONUNIVERSAL FINITE-SIZE EFFECTS NEAR CRITICAL POINTS

We study the finite-size critical behavior of the anisotropic φ⁴ lattice model with periodic boundary conditions in a d-dimensional hypercubic geometry above, at, and below T_c. Our perturbation approach at fixed d = 3 yields excellent agreement with the Monte Carlo (MC) data for the finite-size amplitude of the free energy of the three-dimensional Ising model at T_c by Mon [Phys. Rev. Lett. 54, 2671 (1985)]. Below T_c a minimum of the scaling function of the excess free energy is found. We predict a measurable dependence of this minimum on the anisotropy parameters. Our theory agrees quantitatively with the non-monotonic dependence of the Binder cumulant on the ferromagnetic next-nearest neighbor (NNN) coupling of the two-dimensional Ising model found by MC simulations of Selke and Shchur [J. Phys. A 38, L739 (2005)]. Our theory also predicts a non-monotonic dependence for small values of the anti-ferromagnetic NNN coupling and the existence of a Lifshitz point at a larger value of this coupling. The tails of the large-L behavior at T ≠ T_c violate both finite-size scaling and universality even for isotropic systems as they depend on the bare four-point coupling of the φ⁴ theory, on the cutoff procedure, and on subleading long-range interactions.