Europhys. Lett.
Volume 76, Number 5, December 2006
Page(s) 912 - 918
Section Condensed matter: electronic structure, electrical, magnetic, and optical properties
Published online 03 November 2006
Europhys. Lett., 76 (5), pp. 912-918 (2006)
DOI: 10.1209/epl/i2006-10361-8

Exact results for mean-field zero-temperature random-field Ising model

Dj. Spasojevic, S. Janicevic and M. Knezevic

Faculty of Physics, University of Belgrade - P.O. Box 368, 11000 Belgrade, Serbia

received 5 May 2006; accepted in final form 11 October 2006
published online 3 November 2006

We present an analysis of the dynamical critical behavior of the mean-field zero-temperature random-field Ising model, based on the probability of finding a given sequence in the response signal, which has the form of a Markov chain with Poisson transition probabilities. We provide an exact description of the avalanche duration distribution, the absolute probabilities of signal values, and the signal time-autocorrelation function. The overall behavior of these quantities depends on their characteristic lengths, which all diverge near the critical point (z=1) as $\sim 1/\vert\ln(z)\vert$, where z is a control parameter of the underlying dynamics. Our findings are corroborated with the results of extensive simulations.

75.10.Nr - Spin-glass and other random models.
64.60.Ht - Dynamic critical phenomena.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.

© EDP Sciences 2006