Yielding is an absorbing phase transition with vanishing critical fluctuations

Abstract: 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 ($\beta >1$). We show explicitly that the CDP class is recovered when both properties are relaxed. We locate yielding within a family of models akin to fixed-energy sandpile (FES) models, only with long-range redistribution kernels with zero-modes that result from mechanical equilibrium. For redistribution kernels with sufficiently fast decay, this family of models belong to a short-range universality class distinct from the Conserved Directed Percolation class of usual FES, which is induced by zero modes.