title: Cusps, self-organization, and absorbing states.
abstract: 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.
authors.affiliation: Departamento de Electromagnetismo y Física de la Materia and Instituto de Física Teórica y Computacional Carlos I, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain.
authors.forename: Juan A
authors.initials: JA
authors.lastname: Bonachela
authors.forename: Mikko
authors.initials: M
authors.lastname: Alava
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Muñoz