Phase diagram of gauge glasses

The authors introduce a general class of random spin systems which are symmetric under local gauge transformations. Their model is a generalization of the usual Ising spin glass and includes the Z_q, XY, and SU (2) gauge glasses. For this general class of systems, the internal energy and an upper bound on the specific heat are calculated explicitly in any dimensions on a special line in the phase diagram. Although the line intersects a phase boundary at a multicritical point, the internal energy and the bound on the specific heat are found to be written in terms of a simple function. They also show that the boundary between the ferromagnetic and nonferromagnetic phases is parallel to the temperature axis in the low-temperature region of the phase diagram. This means the absence of re-entrant transitions. All these properties are derived by simple applications of gauge transformations of spin and randomness degrees of freedom.