Critical Ising Spin Dynamics near the Percolation Threshold

A low-temperature approach for the critical Ising spin dynamics on percolation clusters is proposed. The average energy barrier to overturning a cluster of $s$ spins is shown to scale as $\ln s$. This basic result is supported by exact numerical calculations of the energy-barrier distribution for two-and three-dimensional percolation clusters, and is argued to be a consequence of scale invariance. The resulting temperature as well as size dependence of the relaxation-time scales agrees very well with the results of our Monte Carlo simulations.