  We study non-equilibrium phases for interacting two-dimensional
self-propelled particles with isotropic pair-wise interactions using a
persistent kinetic Monte Carlo (MC) approach. We establish the quantitative
phase diagram, including the motility-induced phase separation (MIPS) that is a
commonly observed collective phenomena in active matter. In addition, we
demonstrate for several different potential forms the presence of two-step
melting, with an intermediate hexatic phase, in regions far from equilibrium.
Increased activity can melt a two-dimensional solid and the melting lines
remain disjoint from MIPS. We establish this phase diagram for a range of the
inter-particle potential stiffnesses, and identify the MIPS phase even in the
hard-disk limit. We establish that the full description of the phase behavior
requires three independent control parameters.
