Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-05-17
Journal of Statistical Physics 98 (2000) 103
Physics
Condensed Matter
Statistical Mechanics
30 pages, 10 eps figures
Scientific paper
10.1023/A:1018622805347
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 large negative to positive values. 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 found that for z >3 and for small disorder, the magnetization shows a first order discontinuity for several continuous and unimodel distributions of random fields. The avalanche distribution Prob(s) varies as s^{-3/2} for large s near the discontinuity.
Dhar Deepak
Sabhapandit Sanjib
Shukla Prabodh
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