Dissipationless dynamics of randomly coupled spins at high temperatures

We develop a technique to compute the high-frequency asymptotics of spin correlators in weakly interacting disordered spin systems. We show that the dynamical spin correlator decreases exponentially at high frequencies < SS >(omega) similar to exp(-tau(*)omega) and compute the characteristic time tau* of this dependence. In a typical random configuration, some fraction of spins form strongly coupled pairs, which behave as two- level systems. Their switching dynamics is driven by the high- frequency noise from the surrounding spins, resulting in low- frequency 1/f noise in the magnetic susceptibility and other physical quantities. We discuss application of these results to the problem of susceptibility and flux noise in superconducting circuits at mK temperatures.