  We study a mean-field model of a Kondo alloy using numerical techniques and
analytic approximations. In this model, randomly distributed magnetic
impurities interact with a band of conduction electrons and have a residual
RKKY coupling of strength $J$. This system has a quantum critical point at
$J=J_{c} \sim T_{K}^0$, the Kondo scale of the problem. The $T$ dependence of
the spin susceptibility near the quantum critical point is singular with
$\chi(0)-\chi(T) \propto T^{\gamma}$ and non-integer $\gamma$. At $J_{c}$,
$\gamma = 3/4$. For $J\lesssim J_{c}$ there are two crossovers with decreasing
$T$, first to $\gamma=3/2$ and then to $\gamma=2$, the Fermi-liquid value. The
dissipative part of the time-dependent susceptibility $\chi''(\omega)\propto
\omega$ as $\omega \to 0$ except at the quantum critical point where we find
$\chi''(\omega) \propto \sqrt{\omega}$. The characteristic spin-fluctuation
energy vanishes at the quantum critical point with $\omega_{\rm sf} \sim
(1-J/J_{c})$ for $J\lesssim J_{c}$, and $\omega_{\rm sf} \propto T^{3/2}$ at
the critical coupling.
