  Upon loading, amorphous solids can exhibit brittle yielding, with the abrupt
formation of macroscopic shear bands leading to fracture, or ductile yielding,
with a multitude of plastic events leading to homogeneous flow. It has been
recently proposed, and subsequently questioned, that the two regimes are
separated by a sharp critical point, as a function of some control parameter
characterizing the intrinsic disorder strength and the degree of stability of
the solid. In order to resolve this issue, we have performed extensive
numerical simulations of athermally driven elasto-plastic models with
long-range and anisotropic realistic interaction kernels in two and three
dimensions. Our results provide clear evidence for a finite-disorder critical
point separating brittle and ductile yielding, and we provide an estimate of
the critical exponents in 2D and 3D.
