Distribution of Avalanche Sizes in the Hysteretic Response of the Random-Field Ising Model on a Bethe Lattice at Zero Temperature

Author： Sabhapandit S. Shukla P. Dhar D.

Publisher： Springer Publishing Company

ISSN： 0022-4715

Source： Journal of Statistical Physics, Vol.98, Iss.1-2, 2000-01, pp. : 103-129

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Abstract

We consider the zero-temperature single-spin-flip dynamics of the random-field Ising model on a Bethe lattice in the presence of an external field h. We derive the exact self-consistent equations to determine the distribution Prob(s) of avalanche sizes s as the external field increases from -∞ to ∞. We solve these equations explicitly for a rectangular distribution of the random fields for a linear chain and the Bethe lattice of coordination number z=3, and show that in these cases, Prob(s) decreases exponentially with s for large s for all h on the hysteresis loop. We find that for z4 and for small disorder, the magnetization shows a first-order discontinuity for several continuous and unimodal distributions of the random fields. The avalanche distribution Prob(s) varies as s^-3/2 for large s near the discontinuity.