  We consider a model of an elastic manifold driven on a disordered energy
landscape, with generalized long range elasticity. Varying the form of the
elastic kernel by progressively allowing for the existence of zero-modes, the
model interpolates smoothly between mean field depinning and finite dimensional
yielding. We find that the critical exponents of the model change smoothly in
this process. Also, we show that in all cases the Herschel-Buckley exponent of
the flowcurve depends on the analytical form of the microscopic pinning
potential. This is a compelling indication that within the present
elastoplastic description yielding in finite dimension $d\geq 2$ is a
mean-field transition.
