  We investigate nonequilibrium relaxations of Ising models at the critical
point by using a cluster update. While preceding studies imply that
nonequilibrium cluster-flip dynamics at the critical point are universally
described by the stretched-exponential function, we find that the dynamics
changes from the stretched-exponential to the power function as the
dimensionality is increased: The two-, three-, four-, and infinite-dimensional
Ising models are numerically studied, and the four- and infinite-dimensional
Ising models exhibit the power-law relaxation. We also show that the
finite-size scaling analysis using the normalized correlation length is
markedly effective for the analysis of relaxational processes rather than the
direct use of the Monte Carlo step.
