We combine droplet epitaxy with low-energy electron microscopy imaging techniques to map the surface phase diagram of GaAs(001). The phase patterns produced in droplet epitaxy are interpreted using a simple model which links the spatial coordinates of phase boundaries to the free energy. It is thereby possible to gain important information on surface phase stability, based on the observed sequential order of the phases away from the droplet edge. This can be used to augment existing T=0K phase diagrams generated by density-functional theory calculations. We establish the existence of a (3×6) phase, and confirm that the controversial (6×6) phase is thermodynamically stable over a narrow range of chemical potential.