Bootstrap percolation transition may be first order or second order, or it may have a mixed character where a first-order drop in the order parameter is preceded by critical fluctuations. Recent studies have indicated that the mixed transition is characterized by power-law avalanches, while the continuous transition is characterized by truncated avalanches in a related sequential bootstrap process. We explain this behaviour on the basis of an analytical and numerical study of the avalanche distributions on a Bethe lattice.
KeywordsPercolation bootstrap k-core avalanches power laws fluctuation-driven first-order phase transitions
PACS Nos64.60.ah 64.60.De 64.60.Ht 75.60.Ej 89.75.Da
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