Non-fermi-liquid behavior in a disordered Kondo-alloy model

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 Ruderman-Kittel-Rasuya-Yosida coupling of strength J. This system has a quantum-critical point at J=J(c)similar to T-K(o), 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)proportional to T-gamma and noninteger gamma. At J(c), gamma=3/4. For J less than or similar to 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)proportional to omega as omega-->0 except at the quantum-critical point where we find chi "(omega)proportional to root omega. The characteristic spin-fluctuation energy vanishes at the quantum-critical point with omega(sf)similar to(1 - J/J(c)) for J less than or equal to J(c), and omega(sf)proportional to T-3/2 at the critical coupling. [S0163-1829(99)03131-8].