Critical Ising Spin Dynamics on Percolation Clusters

Ferromagnetically interacting Ising spins are placed on a fractal network (such as a critical percolation cluster) with $T_c=0\mathrm{}$, and endowed with a single-spin-flip dynamics. At low temperatures the collective dynamics is determined by thermal activation over energy barriers. The barrier to overturning of the spins in a domain of size $L$ is proportional to $Z\ln L$, where $Z$ is a new geometrical parameter characterizing the fractal. A new "singular" dynamic scaling is found in which the effective dynamic critical exponent diverges at criticality.