We study a quantum extension of the spherical p-spin-glass model using the imaginary-time replica formalism. We solve the model numerically and we discuss two analytical approximation schemes that capture most of the features of the solution. The phase diagram and the physical properties of the system are determined in thermodynamic equilibrium and under conditions of marginal stability. In both cases, the phase diagram consists of two qualitatively different regions. If the transition temperature is higher than a certain value
T∗, quantum effects are qualitatively irrelevant and the phase transition is second order, as in the classical case. When quantum fluctuations depress the transition temperature below
T∗, the transition becomes first order. The susceptibility is discontinuous and shows hysteresis across the first-order line. This behavior is reminiscent of that observed in the dipolar Ising spin-glass ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}$ in an external transverse magnetic field. We discuss the thermodynamics and the stationary dynamics of both states. The spectrum of magnetic excitations of the equilibrium spin-glass state is gapped, leading to an exponentially small specific heat at low temperatures. That of the marginally stable state is gapless and its specific heat varies linearly with temperature, as generally observed in glasses at low temperature. We show that the properties of the marginally stable state are closely related to those obtained in studies of the real-time dynamics of the system weakly coupled to a quantum thermal bath. Finally, we discuss a possible application of our results to the problem of polymers in random media.
We study a
p-spin spin-glass model to understand if the finite-temperature glass transition found in the mean-field regime of
p-spin models, and used to model the behavior of structural glasses, persists in the nonmean-field regime. By using a three-spin spin-glass model with long-range power-law diluted interactions we are able to continuously tune the (effective) space dimension via the exponent of the interactions. Monte Carlo simulations of the spin-glass susceptibility and the two-point finite-size correlation length show that deep in the nonmean-field regime, the finite-temperature transition is lost whereas this is not the case in the mean-field regime, in agreement with the prediction of Moore and Drossel [Phys. Rev. Lett. 89, 217202 (2002)] that three-spin models are in the same universality class as an Ising spin glass in a magnetic field. However, slightly in the nonmean-field region, we find an apparent transition in the three-spin model, in contrast to results for the Ising spin glass in a field. This may indicate that even larger sizes are needed to probe the asymptotic behavior in this region.
Parisi demonstrated in 1979 that pairwise interactions exhibit a glass spin phase when there is disorder. While he discovered an equilibrium solution of the Sherrington-Kirkpatrick (SK) spin-glass model and we know it as a continuous phase transition, the model dedicated to pairwise interactions and higher-order interactions has not been addressed. This research intends to determine whether this phase exists in triplet interactions. Due to the intractable nature of the three interacting spins alone, we employed a perturbation approach to provide an analytical solution for the triplet interactions in the background of the SK spin-glass model. Our results show the existence of this phase in the third-order interaction and a sudden transition that indicates a change in the nature of a glassy spin system transitioning from the continuous order to the first order. It causes a forward shift in the critical temperature by identifying the frustration of triplet interactions.