Gauge symmetry and its consequences in spin glasses

The model of spin glasses has a symmetry under local change of variables, called gauge symmetry. This symmetry has profound consequences in the determination of the properties of the model. Examples include the exact value of the internal energy, a rigorous bound on the specific heat and the absence of replica symmetry breaking, all on a special submanifold of the phase diagram. It also happens that this whole theoretical framework has a close connection with problems in information science, such as error-correcting codes and image restoration.