Statistical Mechanics of Avalanches
  Statistical mechanics of infinite avalanches is studied in the framework of nonequilibrium random-field Ising model. Critical behavior of the model on a random graph (dilute Bethe lattice) is analyzed in detail. We show that sites with a minimum coordination number 4 play a key role in the occurrence of infinite avalanches. Earlier results which did not seem to fit together very well are explained. 
Prabodh Shukla and Diana Thongjaomayum
cond-mat.stat-mech