  Motivated by recent interest in 2+1 dimensional quantum dimer models, we
revisit Fisher's mapping of two dimensional Ising models to hardcore dimer
models. First, we note that the symmetry breaking transition of the
ferromagetic Ising model maps onto a non-symmetry breaking transition in dimer
language -- instead it becomes a deconfinement transition for test monomers.
Next, we introduce a modification of Fisher's mapping in which a second dimer
model, also equivalent to the Ising model, is defined on a generically
different lattice derived from the dual. In contrast to Fisher's original
mapping, this enables us to reformulate frustrated Ising models as dimer models
with positive weights and we illustrate this by providing a new solution of the
fully frustrated Ising model on the square lattice. Finally, by means of the
modified mapping we show that a large class of three-dimensional Ising models
are precisely equivalent, in the time continuum limit, to particular quantum
dimer models. As Ising models in three dimensions are dual to Ising gauge
theories, this further yields an exact map between the latter and the quantum
dimer models. The paramagnetic phase in Ising language maps onto a deconfined,
topologically ordered phase in the dimer models. Using this set of ideas, we
also construct an exactly soluble quantum eight vertex model.
