Random organization criticality with long-range hydrodynamic interactions

TL;DR

This paper extends the Random Organization Model to include long-range hydrodynamic interactions, revealing how these interactions alter the critical behavior and universality class of the reversible-irreversible transition in driven soft athermal systems.

Contribution

It introduces a generalized ROM with long-range interactions and analyzes how the decay exponent affects the transition's critical properties and universality class.

Findings

Critical properties depend on the decay exponent of interactions.

Transition becomes convex with increasing interaction range.

Hyperuniformity at the transition disappears with long-range interactions.

Abstract

Driven soft athermal systems may display a reversible-irreversible transition between an absorbing, arrested state and an active phase where a steady-state dynamics sets in. A paradigmatic example consists in cyclically sheared suspensions under stroboscopic observation, for which in absence of contacts during a shear cycle particle trajectories are reversible and the stroboscopic dynamics is frozen, while contacts lead to diffusive stroboscopic motion. The Random Organization Model (ROM), which is a minimal model of the transition, shows a transition which falls into the Conserved Directed Percolation (CDP) universality class. However, the ROM ignores hydrodynamic interactions between suspended particles, which make contacts a source of long-range mechanical noise that in turn can create new contacts. Here, we generalize the ROM to include long-range interactions decaying like inverse power laws of the distance. Critical properties continuously depend on the decay exponent when it is smaller than the space dimension. Upon increasing the interaction range, the transition turns convex (that is, with an order parameter exponent $\beta > 1$), fluctuations turn from diverging to vanishing, and hyperuniformity at the transition disappears. We rationalize this critical behavior using a local mean-field model describing how particle contacts are created via mechanical noise, showing that diffusive motion induced by long-range interactions becomes dominant for slowly-decaying interactions.