Ising domain growth barriers on a Cayley Tree at Percolation.

An Ising spin system with ferromagnetic nearest neighbor interactions J is placed on critical percolation clusters on a Cayley tree (i.e., on a Bethe lattice). An energy barrier for a flip between the two ferromagnetically aligned ground states of a cluster of S sites is defined by the process of pushing a domain wall down from the "head" of the tree out through its branches. Two independent calculations indicate that the barrier typically scales as 2J(logS/log4). This is the same form proposed for finite-dimensional percolation clusters; it leads to "singular" dynamic scaling.