  Perovskite solid solutions that have a chemical composition
A(C$_x$D$_{1-x})$O$_3$ with transition metals C and D substitutionally
occupying the B site of a perovskite lattice are attractive in various
applications for their dielectric, piezoelectric and other properties. A
remarkable feature of these solid solutions is the \emph{morphotropic phase
boundary} (MPB), the composition across which the crystal symmetry changes.
Critically, it has long been observed that the dielectric and piezoelectric as
well as the ability to pole a ceramic increases dramatically at the MPB. While
this has motivated much study of perovskite MPBs, a number of important
questions about the role of disorder remain unanswered. We address these
questions using a new approach based on the random-field Ising model with
long-range interactions that incorporates the basic elements of the physics at
the meso-scale. We show that the MPB emerges naturally in this approach as a
frustrated state where stability is exchanged between two well-defined phases.
Specifically, long-range interactions suppress the disorder at compositions
away from MPB but are unable to do so when there is an exchange of stability.
Further, the approach also predicts a number of experimentally observed
features like the fragmented domain patterns and superior ability to pole at
the MPB. The insights from this model also suggest the possibility of entirely
new materials with strong ferroelectric-ferromagnetic coupling using an MPB.
