  A first-principles-derived scheme, that incorporates ferroelectric and
antiferrodistortive degrees of freedom, is developed to study
finite-temperature properties of PbZr1-xTixO3 solid solutions near its
morphotropic phase boundary. The use of this numerical technique (i) resolves
controversies about the monoclinic ground-state for some Ti compositions, (ii)
leads to the discovery of an overlooked phase, and (iii) yields three
multiphase points, that are each associated with four phases. Additional
neutron diffraction measurements strongly support some of these predictions.
