Xs. Chen et V. Dohm, FINITE-SIZE-SCALING IN THE PHI(4) THEORY ABOVE THE UPPER CRITICAL DIMENSION, The European Physical Journal. B: Condensed Matter Physics, 5(3), 1998, pp. 529-542
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.