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-Kasuya-Yosida coupling of strength J. This system has a quantum-critical point at J=Jc~TK⁰, the Kondo scale of the problem. The T dependence of the spin susceptibility near the quantum critical point is singular with χ(0)-χ(T)∝T^γ and noninteger γ. At Jc, γ=3/4. For JJc there are two crossovers with decreasing T, first to γ=3/2 and then to γ=2, the Fermi-liquid value. The dissipative part of the time-dependent susceptibility χ^''(ω)∝ω as →ω0 except at the quantum-critical point where we find χ^''(ω)∝√ω. The characteristic spin-fluctuation energy vanishes at the quantum-critical point with ωsf~(1-J/Jc) for JJc, and ωsf∝T3/2 at the critical coupling.