  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, $<
SS>_{\omega}\sim\exp(-\tau_{*}\omega)$ 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.
