We study a quasistatically driven random-field Ising model (RFIM) at zero temperature with interactions mediated by the long-range anisotropic Eshelby kernel. Analogously to amorphous solids at their yielding transition, and differently from ferromagnetic and dipolar RFIMs, the model shows a discontinuous magnetization jump associated with the appearance of a band-like structure for weak disorder and a continuous magnetization growth, yet punctuated by avalanches, for strong disorder. Through a finite-size scaling analysis in two and three dimensions we find that the two regimes are separated by a finite-disorder critical point, which we characterize. We discuss similarities and differences between the present model and models of sheared amorphous solids.

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• Classical statistical mechanics
• Critical phenomena
• Mechanical deformation
• Finite-size scaling