  We numerically study yielding in two-dimensional glasses which are generated
with a very wide range of stabilities by swap Monte-Carlo simulations and then
slowly deformed at zero temperature. We provide strong numerical evidence that
stable glasses yield via a nonequilibrium discontinuous transition in the
thermodynamic limit. A critical point separates this brittle yielding from the
ductile one observed in less stable glasses. We find that two-dimensional
glasses yield similarly to their three-dimensional counterparts but display
larger sample-to-sample disorder-induced fluctuations, stronger finite-size
effects, and rougher spatial wandering of the observed shear bands. These
findings strongly constrain effective theories of yielding.
