  We investigate the dynamic critical exponent of the two-dimensional Ising
model defined on a curved surface with constant negative curvature. By using
the short-time relaxation method, we find a quantitative alteration of the
dynamic exponent from the known value for the planar Ising model. This
phenomenon is attributed to the fact that the Ising lattices embedded on
negatively curved surfaces act as ones in infinite dimensions, thus yielding
the dynamic exponent deduced from mean field theory. We further demonstrate
that the static critical exponent for the correlation length exhibits the mean
field exponent, which agrees with the existing results obtained from canonical
Monte Carlo simulations.
