From second to first order transitions in a disordered quantum magnet

We study the spin-glass transition in a disordered quantum model. In a regi on of the phase diagram quantum effects are small and the phase transition is second order, as in the classical case. In another region, quantum fluct uations drive the transition to first order. Across the first order line th e susceptibility is discontinuous and shows hysteresis. Our findings qualit atively reproduce observations on LiHoxY1-xF4. We also discuss a marginally stable spin-glass state and derive some results previously obtained from t he real-time dynamics of the model coupled to a bath.