### Abstract

The approach to equilibrium at the
critical temperature of the two-dimensional Ising model from an
initial ordered spin configuration is investigated using the single
cluster Monte Carlo dynamics introduced by Wolff. An initial
configuration of all up spins and its dual, a checkerboard
state, are considered. We give simple mean-field and scaling
arguments for the existence of power-law decay. Because the usual
arguments for time rescaling might not be applicable when the system
is approaching equilibrium, we directly determine the relation of
the number of cluster flips to the number of Monte Carlo steps per
spin. For both initial configurations we find that the effective
dynamical critical exponent determined from the power-law behavior
and the proper time rescaling differs from the estimates of the
equilibrium dynamical exponent and depends on the initial conditions
for the system sizes and times we have investigated.