Cusps, self-organization, and absorbing states

TL;DR

This paper demonstrates that systems with many absorbing states and conservation laws, even without quenched disorder, exhibit cusp singularities similar to those in elastic interfaces with quenched disorder, revealing universal features of criticality.

Contribution

It shows that cusp singularities occur in annealed systems with absorbing states and conservation laws, extending the understanding of critical phenomena beyond quenched disorder.

Findings

Systems with absorbing states exhibit cusp singularities.

Different types of cusps are identified in conserved and non-conserved systems.

A new experimental protocol inspired by self-organized criticality is proposed.

Abstract

Elastic interfaces embedded in (quenched) random media exhibit meta-stability and stick-slip dynamics. These non-trivial 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 non-conserved 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.