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We present exact results for the critical behavior of the RFIM on completegraphs and trees, both at equilibrium and away from equilibrium, i.e., modelsfor hysteresis and Barkhausen noise. We show that for stretched exponential andpower law distributions of random fields the behavior on complete graphs isnon-universal, while the behavior on Cayley trees is universal even in thelimit of large co-ordination.Comment: 4 pages, 4 figure

Random-field Ising model on complete graphs and trees