## Low-temperature phase diagrams of quantum lattice systems. I. Stability for quantum perturbations of classical systems with finitely-many ground states

Starting from classical lattice systems in d {ge} 2 dimensions with a regular zero-temperature phase diagram, involving a finite number of periodic ground states, we prove that adding a small quantum perturbation and/or increasing the temperature produce only smooth deformations of their phase diagrams. The quantum perturbations can involve bosons or fermions and can be of infinite range but decaying exponentially fast with the size of the bonds. For fermions, the interactions must be given by monomials of even degree in creation and annihilation operators. Our methods can be applied to some anyonic systems as well. Our analysis is basedmore »