Gauge theory of amorphous magnets

A gauge theory of disordered magnets as a field theory in the principal fiber bundle with structure group $SL(3,R)$ is constructed. The gauge field interacting with a vector field (the magnetization) is responsible for the disorder. A complete system of equations, valid for arbitrary disordered magnets, is obtained. In the limiting case of a free gauge field the proposed approach leads to the well-known Volovik–Dzyaioshinskii theory, which describes isotropic spin glasses. In the other limiting case when the curvature is zero the results of Ignatchenko and Iskhakov for weakly disordered ferromagnets are reproduced.