  We propose a new quantum model interpolating between the fully frustrated
spin-1/2 Ising model in a transverse field and a dimer model. This model
contains a resonating-valence-bond phase, including a line with an exactly
solvable ground state of the Rokhsar-Kivelson type. We discuss the phase
diagrams of this model on the square and triangular (in terms of the dimer
representation) lattices.
