Droplets in Disordered Metallic Quantum Critical Systems

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We present a field theory for a structurally disordered magnetic system coupled to a metallic environment near a quantum critical point. We show that close to the magnetic quantum critical point droplets are formed due to the disorder and undergo dissipative quantum dynamics. We show that the problem has a characteristic energy scale, the droplet Kondo temperature, that determines the crossover energy scale from weak to strong coupling. Our results have direct significance for the Griffiths-McCoy singularities of itinerant magnets.