Using Monte Carlo simulations we show that for 2D and 3D Ising models at ze
ro temperature the average life-time tau of a square/cubic-like domain of t
he linear size L is proportional to L-2. However, for certain initial confi
gurations tau increases much faster: it scales as L-3 for the 2D model and
for the 3D case the increase is even faster. We suggest that such a scaling
is responsible for some anomalies of the phase-ordering kinetics in this m
odel. (C) 1999 Elsevier Science B.V. All rights reserved.