  We revisit the phase diagram of Rokhsar-Kivelson models, which are used in
fields such as superconductivity, frustrated magnetism, cold bosons, and the
physics of Josephson junction arrays. From an extended height effective theory,
we show that one of two simple generic phase diagrams contains a mixed phase
that interpolates continuously between columnar and plaquette states. For the
square lattice quantum dimer model we present evidence from exact
diagonalization and Green's function Monte Carlo techniques that this scenario
is realised, by combining an analysis of the excitation gaps of different
symmetry sectors with information on plaquette structure factors. This presents
a natural framework for resolving the disagreement between previous studies.
