Yielding is an absorbing phase transition with vanishing critical fluctuations

The yielding transition in athermal complex fluids can be interpreted as an absorbing phase transition between an elastic, absorbing state with high mesoscopic degeneracy and a flowing, active state. We characterize quantitatively this phase transition in an elastoplastic model under fixed applied shear stress, using a finite-size scaling analysis.

We find vanishing critical fluctuations of the order parameter (i.e., the shear rate), and relate this property to the convex character of the phase transition. Exponent values strongly differ from that of Conserved Directed Percolation (CDP), the expected universality class for systems with infinitely many absorbing states. This discrepancy is traced back to two key physical ingredients: the long-range character of elastic interactions and zero-sum constraints on the elastic propagator, both resulting from mechanical equilibrium. We show explicitly that the CDP class is recovered when both properties are relaxed. Our work also suggests the existence of an additional universality class, different from CDP, for sand-pile-type models with specific constraints on the short-range redistribution kernel.