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Physical review. B, Condensed matter

Quantum orientational glasses: Large-Mlimit approach

T. K. Kopeć

Published Aug 1, 1996• 7 citations
Publisher

Abstract

We study a generalization of the quantum model of fully isotropic uniaxial p-polar glasses with multicomponent orientational degrees of freedom and Gaussian-distributed random, infinite-range exchange interactions. The quantum effects are associated with a finite moment of inertia (treated quantum mechanically) of a particle with M orientational degrees of freedom. The system exhibits a quantum phase transition separating the glassy and paraorientational phases regulated by a parameter \ensuremath{\Delta} (inverse of the moment of inertia of a particle). The model allows in the limit M\ensuremath{\rightarrow}\ensuremath{\infty} for an exact solution both in the glassy and disordered phases for an arbitrary value of the parameter p. We have analytically established the closed form of the self-consistency solution for the dynamic order parameter within the replica method and show that different spin glass transition scenarios emerge as a function of the parameter p. Whereas for p=1 (dipolar case) the solution of the quantum glass model is exact within replica symmetry, with a continuous phase transition along the critical line ${\mathit{T}}_{\mathit{c}}$(\ensuremath{\Delta}) we showed that the model for p\ensuremath{\ge}2 (multipolar case) undergoes a first-order phase transition. In the latter case within the Parisi replica-symmetry-breaking scheme we have determined a functional Parisi-like order parameter q(x) and demonstrated that for p\ensuremath{\ge}2 a single step of the replica symmetry breaking is the exact solution within the glassy phase. For the physically most relevant case of p=2 (quantum quadrupolar glass) the \ensuremath{\Delta}-T phase diagram has been computed numerically. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.3367

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We study a generalization of the quantum model of fully isotropic uniaxial p-polar glasses with multicomponent orientational degrees of freedom and Gaussian-distributed random, infinite-range exchange interactions. The quantum effects are associated with a finite moment of inertia (treated quantum mechanically) of a particle with M orientational degrees of freedom. The system exhibits a quantum phase transition separating the glassy and paraorientational phases regulated by a parameter \ensuremath{\Delta} (inverse of the moment of inertia of a particle). The model allows in the limit M\ensuremath{\rightarrow}\ensuremath{\infty} for an exact solution both in the glassy and disordered phases for an arbitrary value of the parameter p. We have analytically established the closed form of the self-consistency solution for the dynamic order parameter within the replica method and show that different spin glass transition scenarios emerge as a function of the parameter p. Whereas for p=1 (dipolar case) the solution of the quantum glass model is exact within replica symmetry, with a continuous phase transition along the critical line Tc{\mathit{T}}_{\mathit{c}}Tc​(\ensuremath{\Delta}) we showed that the model for p\ensuremath{\ge}2 (multipolar case) undergoes a first-order phase transition. In the latter case within the Parisi replica-symmetry-breaking scheme we have determined a functional Parisi-like order parameter q(x) and demonstrated that for p\ensuremath{\ge}2 a single step of the replica symmetry breaking is the exact solution within the glassy phase. For the physically most relevant case of p=2 (quantum quadrupolar glass) the \ensuremath{\Delta}-T phase diagram has been computed numerically. \textcopyright{} 1996 The American Physical Society.
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We determine the low-energy spectrum and Parisi replica-symmetry-breaking function for the spin-glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal ( h ) fields. We show that, for all h , the spin-glass state has full replica symmetry breaking and the local spin spectrum is gapless, with a spectral density that vanishes linearly with frequency. These results are obtained using an action functional—argued to yield exact results at low frequencies—that expands in powers of a spin-glass order parameter, which is bilocal in time, and a matrix in replica space. We also present the exact solution of the infinite-range spherical quantum p -rotor model at nonzero h : here, the spin-glass state has one-step replica symmetry breaking and gaplessness only appears after imposition of an additional marginal stability condition. Possible connections to experiments on random arrays of trapped Rydberg atoms are noted. Published by the American Physical Society 2024
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∗,{T}^{*},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∗,{T}^{*},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.
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