On the phase transition of the Ising gauge model

We study the Ising gauge model in dimensionsD2. In addition to the plaquette coupling of this model we introduce a nearest neighbour ferromagnetic Ising coupling. By that means the local gauge symmetry is removed while the global symmetry of the Ising model is still present. The phase diagram of the model is found by using general arguments as well as Monte-Carlo methods. The gauge phase of the model is characterized by the presence of a topological excitation (defect) which has no influence on any local physical quantity.