  We investigate the critical behaviour of the two-dimensional Ising model
defined on a curved surface with a constant negative curvature. Finite-size
scaling analysis reveals that the critical exponents for the zero-field
magnetic susceptibility and the correlation length deviate from those for the
Ising lattice model on a flat plane. Furthermore, when reducing the effects of
boundary spins, the values of the critical exponents tend to those derived from
the mean field theory. These findings evidence that the underlying geometric
character is responsible for the critical properties the Ising model when the
lattice is embedded on negatively curved surfaces.
