Multiplicative Noise and Second Order Phase Transitions

Alon Manor, Nadav M. Shnerb

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20 Scopus citations


The scale-free distribution of cluster sizes in continuous phase transitions is linked to the law of proportional effect. A numerical study of a two-dimensional Ising model suggests that a cluster size undergoes a multiplicative birth-death process. At the transition the ratio between birth and death rates approaches unity for large clusters, and the resulting steady state shows a power-law behavior. The percolation dynamic, on the other hand, yields a geometric phase transition without ergodicity breaking, where large-scale merging and splitting of clusters dominate the distribution. Instead of short-range birth-death jumps, the percolation transition is characterized by Lévi flights along the cluster-size axis.

Original languageEnglish
Article number030601
JournalPhysical Review Letters
Issue number3
StatePublished - 17 Jul 2009


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