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We discuss the behavior of a quantum glassy system coupled to a bath of quantum oscillators. We show that the system localizes in the absence of interactions when coupled to a subOhmic bath. When interactions are switched on localization disappears and the system undergoes a phase transition towards a glassy phase. We show that the position of the critical line separating the disordered and the ordered phases strongly depends on the coupling to the bath. For a given type of bath, the ordered glassy phase is favored by a stronger coupling. Ohmic, subOhmic and superOhmic baths lead to different transition lines. We draw our conclusions from the analysis of the partition function using the replicated imaginary-time formalism and from the study of the real-time dynamics of the coupled system using the Schwinger-Keldysh closed time-path formalism.Comment: 39 pages, 13 figures, RevTe

The long-time dynamics of the critical contact process which is brought suddenly out of an uncorrelated initial state undergoes ageing in close analogy with quenched magnetic systems. In particular, we show through Monte Carlo simulations in one and two dimensions and through mean-field theory that time-translation invariance is broken and that dynamical scaling holds. We find that the autocorrelation and autoresponse exponents λ Γ and λ R are equal but, in contrast to systems relaxing to equilibrium, the ageing exponents a and b are distinct. A recent proposal to define a non-equilibrium temperature through the short-time limit of the fluctuation-dissipation ratio is therefore not applicable.

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.