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Physical review. B, Condensed matter

Cavity-fields approach to quantumXYspin-glass models in a transverse field

L. De Cesare, K. Lukierska‐Walasek, Ileana Rabuffo, Katarzyna Walasek

Published Jan 1, 1992• 14 citations
Publisher

Abstract

The cavity-fields approach, recently developed for studying the Sherrington-Kirkpatrick model of spin glasses and its quantum version, is appropriately reformulated for the infinite-range XY spin-glass model in a transverse field. The equations for the phase diagram of the model are obtained and preliminary numerical results are also presented.

DOI
10.1103/physrevb.45.1041

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Communications in Theoretical Physics•Mar 1, 1991•0 citations
The cavity-fields approach, recently developed for studying the Sherrington-Kirkpatrick model of spin glasses and its quantum version, is appropriately reformulated for the infinite-range XY spin-glass model in a transverse field. The equations for the phase diagram of the model are obtained and preliminary numerical results are also presented.
The cavity-field method, recently used for classical spin glasses, is extended to study the infinite-range Ising spin-glass model in a transverse field, by means of the Trotter-Suzuki transformation. Within this approach, which relies on well-known mathematics and deals with quantities that have transparent physical significance by avoiding the replica method, the quantum version of the classical Thouless-Anderson-Palmer equation is obtained. The phase diagram of the model is also obtained and full agreement with previous replica-method results is found.
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 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 LiHo0.167{\mathrm{LiHo}}_{0.167}LiHo0.167​Y0.833{\mathrm{Y}}_{0.833}Y0.833​F4{\mathrm{F}}_{4}F4​, 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.