Non-linear sigma model study of magnetic dephasing in a mesoscopic spin glass

We propose a nonlinear sigma model for the description of quantum transport in a mesoscopic metallic conductor with magnetic impurities frozen in a spin glass phase. It accounts for the presence of both the corresponding scalar and magnetic random potentials. In a spin glass, this magnetic random potential is correlated between different realizations. As the strength of the magnetic potential is varied, this model describes the crossover between orthogonal and unitary universality classes of the nonlinear sigma model. We apply this technique to the calculations of the correlation of conductance between two frozen spin configurations in terms of dephasing rates for the usual low energy modes of weak localization theory.