  Ising models of emergent geometry are well known to possess ground states
with many of the desired features of a low dimensional, Ricci flat vacuum.
Further, excitations of these ground states can be shown to replicate the
quantum dynamics of a free particle in the continuum limit. It would be a
significant next step in the development of emergent Ising models to link them
to an underlying physical theory that has General Relativity as its continuum
limit. In this work we investigate how the canonical formulation of General
Relativity can be used to construct such a discrete Hamiltonian using recent
results in discrete differential geometry. We are able to demonstrate that the
Ising models of emergent geometry are closely related to the model we propose,
which we term the Canonical Ising Model, and may be interpreted as an
approximation of discretized canonical general relativity.
