  We investigate the dual of the kappa=0 Gonihedric Ising model on a 3D cubic
lattice, which may be written as an anisotropically coupled Ashkin-Teller
model. The original kappa=0 Gonihedric model has a purely plaquette
interaction, displays a first order transition and possesses a highly
degenerate ground state.
  We find that the dual model admits a similar large ground state degeneracy as
a result of the anisotropic couplings and investigate the coupled mean field
equations for the model on a single cube. We also carry out Monte Carlo
simulations which confirm a first order phase transition in the model and
suggest that the ground state degeneracy persists throughout the low
temperature phase. Some exploratory cooling simulations also hint at
non-trivial dynamical behaviour.
