Phase diagram of gauge glasses

Abstract

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 Zq, 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.