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

From Second to First Order Transitions in a Disordered Quantum Magnet