  We review recent results concerning finite size corrections to the Ising
model free energy on lattices with non-trivial topology and curvature. From
conformal field theory considerations two distinct universal terms are
expected, a logarithmic term determined by the system curvature and a scale
invariant term determined by the system shape and topology. Both terms have
been observed numerically, using the Kasteleyn Pfaffian method, for lattices
with topologies ranging from the sphere to that of a genus two surface. The
constant term is shown to be expressible in terms of Riemann theta functions
while the logarithmic correction reproduces the theoretical prediction by Cardy
and Peschel for singular metrics.
