Thomas P Handford, Francisco J Perez-Reche, Sergei N Taraskin
A mapping of avalanches occurring in the zero-temperature random-field Ising model (zt-RFIM) to life-periods of a population experiencing immigration is established. Such a mapping allows the microscopic criteria for occurrence of an infinite avalanche in a q-regular graph to be determined. Based on these criteria, we explain why an infinite avalanche can occur only for q>3. A key factor for an avalanche to become infinite is that it interacts in an optimal way with previously flipped spins. The generating function techniques developed for branching processes are applied to obtain expressions analytically for the duration, pulse-shapes and power spectrum of the avalanches. The results show that only very long avalanches exhibit a significant degree of universality.
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http://arxiv.org/abs/1302.7027
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