Cusps, self-organization, and absorbing states

Bonachela, Juan A. and Alava, Mikko and Muñoz, Miguel A. (2009) Cusps, self-organization, and absorbing states. Physical Review E, 79 (5). 050106. ISSN 2470-0053 (

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Elastic interfaces embedded in (quenched) random media exhibit metastability and stick-slip dynamics. These nontrivial dynamical features have been shown to be associated with cusp singularities of the coarse-grained disorder correlator. Here we show that annealed systems with many absorbing states and a conservation law but no quenched disorder exhibit identical cusps. On the other hand, similar nonconserved systems in the directed percolation class are also shown to exhibit cusps but of a different type. These results are obtained both by a recent method to explicitly measure disorder correlators and by defining an alternative new protocol inspired by self-organized criticality, which opens the door to easily accessible experimental realizations.