  The free energy of a two-dimensional system at criticality has in general an
universal part proportional the logarithm of the system size. This term was
shown by Cardy and Peschel to be related to the curvature of the system, with
smooth metrics and singular points contributing in distinct ways. In this paper
we present a numerical study of the effect, for the Ising model on lattices
with various topologies from the sphere to genus two surfaces. The nature of
this term for specific lattice models is an open problem because the
distinction between the two kinds of contributions involves an interchange of
the limit of singular curvature with the thermodynamic limit. For all the
lattices studied we found precise agreement with the conformal field theory
prediction for conical singularities.
