The non-equilibrium critical relaxation of the single-cluster dynamics
is studied for the ferromagnetic Ising model on the square and cubic
lattices. Power-law behavior is observed in the energy relaxation proc
ess starting from an all-up spin configuration. From this power decay,
the dynamical exponent z is estimated to be 0.50 +/- 0.05 and 1.3 +/-
0.1 for the square and cubic lattices, respectively, where the time i
s defined by the number of cluster flip trials. If the time scale is n
ormalized by cluster mass, they are 0.25 +/- 0.05 and 0.3 +/- 0.1, res
pectively.