  We show how to construct space time lattices with a Regge action proportional
to the energy of a given Ising or Potts model macrostate. This allows to take
advantage of the existence of exact solutions for these models to calculate the
quantum wave function of the universe using the sum over the histories approach
to quantum gravity. Motivated by this isomorphism we show how the Regge
equations, i.e. the discrete equivalent of the vacuum Einstein equations, can
be derived using statistical mechanics under the assumption that the energy of
a given space time geometry is proportional to the Regge action.
