Quadratic contact process: phase separation with interface-orientation-dependent equistability

The quadratic contact process is implemented on a square lattice as a model with random adsorption and correlated desorption requiring empty pairs of diagonal neighbors. The model exhibits a discontinuous phase transition between an active state and an absorbing state, but equistability between these states depends on the orientation of the separating interface. Correspondingly, for a generalized class of models, we find phase coexistence over a finite region of their two-dimensional parameter space. This is in stark contrast to behavior in equilibrium systems.