A Gauge Invariant Dual Gonihedric 3D Ising Model
  We note that two formulations of dual gonihedric Ising models in 3d, one based on using Wegner's general framework for duality to construct a dual Hamiltonian for codimension one surfaces, the other on constructing a dual Hamiltonian for two-dimensional surfaces, are related by a variant of the standard decoration/iteration transformation.   The dual Hamiltonian for two-dimensional surfaces contains a mixture of link and vertex spins and as a consequence possesses a gauge invariance which is inherited by the codimension one surface Hamiltonian. This gauge invariance ensures the latter is equivalent to a third formulation, an anisotropic Ashkin-Teller model. We describe the equivalences in detail and discuss some Monte-Carlo simulations which support these observations. 
D. A. Johnston, R. P. K. C. M. Ranasinghe
cond-mat.stat-mech