Mechanisms of evolution of avalanches in regular graphs

Thomas P. Handford, Francisco J. Perez-Reche, Sergei N. Taraskin

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


A mapping of avalanches occurring in the zero-temperature random-field Ising model to life periods of a population experiencing immigration is established. Such a mapping allows the microscopic criteria for the occurrence of an infinite avalanche in a q-regular graph to be determined. A key factor for an avalanche of spin flips to become infinite is that it interacts in an optimal way with previously flipped spins. Based on these criteria, we explain why an infinite avalanche can occur in q-regular graphs only for q>3 and suggest that this criterion might be relevant for other systems. The generating function techniques developed for branching processes are applied to obtain analytical expressions for the durations, pulse shapes, and power spectra of the avalanches. The results show that only very long avalanches exhibit a significant degree of universality.
Original languageEnglish
Article number 062122
Number of pages10
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number6
Publication statusPublished - Jun 2013


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