Dynamics of a quantum phase transition in the random Ising model: Logarithmic dependence of the defect density on the transition rate

A quantum phase transition from paramagnetic to ferromagnetic phase is driven by a time-dependent external magnetic field. For any rate of the transition the evolution is nonadiabatic and finite density of defects is excited in the ferromagnetic state. The density of excitations has only logarithmic dependence on the transition rate. This is qualitatively different than any usual power law scaling predicted for pure systems by the Kibble-Zurek mechanism. No matter how slow the transition is the defect density remains more or less the same.