  We study the mean-field limit of an elasto-plastic model introduced to
describe the yielding transition of athermally and quasi-statically sheared
amorphous solids. We focus on the sample-to-sample fluctuations, which we
characterize analytically, and investigate in detail the analogy with the
athermally driven random-field Ising model. We stress that the random field at
the yielding transition is an emerging disorder and we investigate the various
factors that determine its strength.
