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The yielding transition in athermal complex fluids can be interpreted as anabsorbing phase transition between an elastic, absorbing state with highmesoscopic degeneracy and a flowing, active state. We characterizequantitatively this phase transition in an elastoplastic model under fixedapplied shear stress, using a finite-size scaling analysis. We find vanishingcritical fluctuations of the order parameter (i.e., the shear rate), and relatethis property to the convex character of the phase transition ($\beta >1$). Weshow explicitly that the CDP class is recovered when both properties arerelaxed. We locate yielding within a family of models akin to fixed-energysandpile (FES) models, only with long-range redistribution kernels withzero-modes that result from mechanical equilibrium. For redistribution kernelswith sufficiently fast decay, this family of models belong to a short-rangeuniversality class distinct from the Conserved Directed Percolation class ofusual FES, which is induced by zero modes.

Yielding is an absorbing phase transition with vanishing critical fluctuations