We derive exact results for several thermodynamic quantities of the O
(
n
) symmetric
field theory in the limit
in a finite d-dimensional hypercubic geometry with periodic boundary conditions. Corresponding results are derived for an O
(
n
) symmetric
model on a finite d-dimensional lattice with a finite-range interaction. The leading finite-size effects near Tc of the field-theoretic model are compared with those of the lattice model. For 2 <
d
< 4, the finite-size scaling functions are verified to be universal. For d
> 4, significant lattice effects are found. Finite-size s...
