Lattice φ4 theory of finite-size effects above the upper critical dimension

We present a perturbative calculation of finite-size effects near T-c of the phi(4) lattice model in a d-dimensional cubic geometry of size L with periodic boundary conditions for d > 4. The structural differences between the phi(4) lattice theory and the phi(4) held theory found previously in the spherical limit are shown to exist also for a finite number of components of the order parameter. The two-variable finite-size scaling functions of the field theory are nonuniversal whereas those of the lattice theory are independent of the nonuniversal model parameters. One-loop results for finite-size scaling functions are derived. Their structure disagrees with the single-variable scaling form of the lowest-mode approximation for any finite xi/L where xi is the bulk correlation length. At T-c, the large-L behavior becomes lowest-mode like for the lattice model but not for the field-theoretic model. Characteristic temperatures close to T-c of the lattice model, such as T-max(L) of the maximum of the susceptibility chi, are found to scale asymptotically as T-c- T-max(L) similar to L-d/2, in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising model. We also predict chi(max) similar to L-d/2 asymptotically. On a quantitative level, the asymptotic amplitudes of this large-L behavior close to T-c have not been observed in previous MC simulations at d = 5 because of nonnegligible finite-size terms similar to L(4-d/2) caused by the inhomogeneous modes. These terms identify the possible origin of a significant discrepancy between the lowest-mode approximation and previous MC data. MC data of larger systems would be desirable for testing the magnitude of the L(4-d/2) and L4-d terms predicted by our theory.