Yielding versus random organization: convex absorbing transitions in soft matter

Abstract We explore the similarities and differences in the behavior of two different soft matter models, a generalized random organization model describing the stroboscopic dynamics of cyclically sheared suspensions, and an elastoplastic model describing the mesoscale dynamics of a yield-stress fluid under imposed stress. Both systems can be described in the framework of absorbing phase transitions (APTs), which are nonequilibrium phase transitions between an absorbing (frozen) phase and an active phase. In both models, a peculiar mechanism is at work: activity induces an internal noise which is transmitted over large distances by long-ranged mediated interactions, either hydrodynamic or elastic, which results in non-local creation of activity. This microscopic similarity is echoed in the critical behavior, as in both cases the transitions are convex, i.e. the order parameter (here the mean activity) is convex as a function of the control parameter (i.e. the exponent β > 1 ). This is in stark contrast with usual APT, like (Conserved) directed percolation, which are concave ( β < 1 ). Taking the power-law decay exponent α of long-range interactions as a control parameter, we compare the dependence of the critical properties (activity mean value and fluctuations, avalanche statistics, low-wavenumber structure factor) on the decay exponent α in both models, finding a qualitatively similar scenario. A smooth crossover is observed as a function of α between a concave transition regime for short-range interactions, with diverging fluctuations and compact avalanches, and a convex transition regime, with vanishing fluctuations and non-compact avalanches, for longer-range interactions. Although for a given range exponent α , the values of critical exponents for both models differ, a good agreement between the models is found by parametrically plotting the different critical exponents as a function of the exponent β of the mean activity. In this parametric representation, the concave regime is consistent with the behavior of the long-range directed percolation class, while the convex regime can be accounted for by a mean-field-type scenario with anomalous diffusion close to an absorbing boundary, inspired by the Hébraud–Lequeux model for the yielding transition.