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arXiv:cond-mat/9312036 · Physical review. B, Condensed matter

Ising spin glass in a transverse magnetic field

B. Boechat, Raimundo R. dos Santos, M. A. Contínentino

Published Mar 1, 1994• 25 citations
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Abstract

We study the three-dimensional quantum Ising spin glass in a transverse magnetic field following the evolution of the bond probability distribution under renormalization-group transformations. The phase diagram (critical temperature ${\mathit{T}}_{\mathit{c}}$ vs transverse field \ensuremath{\Gamma}) we obtain shows a finite slope near T=0, in contrast with the infinite slope for the pure case. Our results compare very well with the experimental data recently obtained for the dipolar Ising spin glass ${\mathrm{LiHo}}_{0.167}$${\mathrm{Y}}_{0.833}$${\mathrm{F}}_{4}$, in a transverse field. This indicates that this system is more appropriately described by a model with short-range interactions than by an equivalent Sherrington-Kirkpatrick model in a transverse field.

DOI
10.1103/physrevb.49.6404

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We study the three-dimensional quantum Ising spin glass in a transverse magnetic field following the evolution of the bond probability distribution under renormalization-group transformations. The phase diagram (critical temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ vs transverse field \ensuremath{\Gamma}) we obtain shows a finite slope near T=0, in contrast with the infinite slope for the pure case. Our results compare very well with the experimental data recently obtained for the dipolar Ising spin glass {\mathrm{LiHo}}_{0.167}$${\mathrm{Y}}_{0.833}$${\mathrm{F}}_{4}, in a transverse field. This indicates that this system is more appropriately described by a model with short-range interactions than by an equivalent Sherrington-Kirkpatrick model in a transverse field.
The infinite-range Ising spin-glass in the presence of a transverse field is studied by Monte Carlo simulations. The overlap probability distribution P ( q ) is defined and calculated for the present quantum case. The P ( q ) in the spin-glass phase has a long tail extended down to q = 0 qualitatively similar to the classical Sherrington-Kirkpatrick model. The phase boundary of the glass transition temperature vs. the transverse field is obtained. Our results for the phase diagram agree with our recent replica symmetry-breaking solution but disagree with the results of Yokata and of Ray et al.
We present results of a Monte Carlo simulation study of the zero-temperature quantum phase transition of a three-dimensional short-range spin-1/2 Ising spin glass, driven by a transverse magnetic field. This quantum transition is equivalent to the finite-temperature transition in the (3+1)-dimensional anisotropic classical random Ising model that is the path integral of the quantum system. The critical exponents are estimated using a finite-size scaling analysis. The uniform linear susceptibility is finite at the transition, while the nonlinear susceptibility diverges. The results are more consistent with conventional, rather than activated, dynamic scaling in the quantum system.
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We use quantum Monte Carlo methods and various analytic approximations to study the infinite-range Ising spin-glass model in a transverse field in the disordered phase. We focus on the behavior of the frequency dependent susceptibility of the system above and below the critical field. We establish that, at the quantum critical point, there exists an equivalence between the long-time behavior of this model and that of the single-impurity Kondo model. Our predictions for the long-time dynamics of the model are in good agreement with experimental results on LiHo0.167Y0.833F4{\mathrm{LiHo}}_{0.167}{\mathrm{Y}}_{0.833}{\mathrm{F}}_{4}LiHo0.167​Y0.833​F4​.