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We study the mean-field limit of an elasto-plastic model introduced todescribe the yielding transition of athermally and quasi-statically shearedamorphous solids. We focus on the sample-to-sample fluctuations, which wecharacterize analytically, and investigate in detail the analogy with theathermally driven random-field Ising model. We stress that the random field atthe yielding transition is an emerging disorder and we investigate the variousfactors that determine its strength.

Emergence of a random field at the yielding transition of a mean-field Elasto-Plastic model