Criteria for infinite avalanches in the zero-temperature nonequilibrium random-field Ising model on a Bethe lattice.

We present general criteria for the occurrence of infinite avalanches and critical hysteresis in the zero-temperature nonequilibrium random-field Ising model on a Bethe lattice. Drawing upon extant results as well as a result on a dilute four-coordinated (z=4) lattice, we show that diverging avalanches can occur if an arbitrarily small fraction of sites on a spanning cluster have connectivity z≥4.