Space-time phase transitions in the East model with a softened kinetic constraint

The East model has a dynamical phase transition between an active (fluid) and inactive (glass) state. We show that this phase transition generalizes to "softened" systems where constraint violations are allowed with small but finite probabilities. Moreover, we show that the first order coexistence line separating the active and inactive phases terminates in a finite-temperature space-time critical point. Implications of these results for equilibrium dynamics are discussed.