FINITE-SIZE-SCALING IN THE PHI(4) THEORY ABOVE THE UPPER CRITICAL DIMENSION

We derive exact results for several thermodynamic quantities of the O( n) symmetric phi(4) field theory in the limit n --> infinity in a fini te d-dimensional hypercubic geometry with periodic boundary conditions . Corresponding results are derived for an O(n) symmetric phi(4) model on a finite d-dimensional lattice with a finite-range interaction. Th e leading finite-size effects near T-c of the field-theoretic model ar e compared with those of the lattice model. For 2 < d < 4, the finite- size scaling functions are verified to be universal. For d > 4, signif icant lattice effects are found. Finite-size scaling in its usual simp le form does not hold for d > 4 but remains valid in a generalized for m with two reference lengths. The finite-size scaling functions of the phi(4) field theory turn out to be nonuniversal whereas those of the phi(4) lattice model are independent of the nonuniversal model paramet ers. In particular, the field-theoretic model exhibits finite-size eff ects whose leading exponents differ from those of the lattice model. T he widely accepted lowest-mode approach is shown to fail for both the field-theoretic and the lattice model above four dimensions.