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Physical review. B, Condensed matter

Cavity-field approach to quantum spin glasses: The Ising spin glass in a transverse field

L. De Cesare, Katarzyna Walasek, K. Walasek

Published Apr 1, 1992• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.45.8127

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Europhysics Letters (EPL)•Oct 15, 1990•19 citations
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.
In this paper we derive an expression for the free energy of the infinite ranged quantum Potts spin-glass in a transverse field using the replica method and the Suzuky-Trotter formula. Results are obtained for general p (number of Potts states) and explicit calculations are done for p=3 using exact spin summations for M≤8 where M is the size of the lattice in the Trotter direction. The phase diagram is obtained and is also compared with results for the static approximation which is non trivial even in the paramagnetic phase.
The infinite-range Ising spin glass in the presence of a transverse field is considered. Using the generalised Trotter formula and replica methods, the free energy for the system with quenched random bond interactions is evaluated using the static approximation. It is shown that, when the strength of the transverse field equals the largest eigenvalue of the random bond interaction matrix, the spin glass transition is destroyed. The authors also show that a replica-symmetric spin glass phase is stable in a certain region of the temperature-field phase diagram. Finally they present suggestive arguments which indicate that, when the time dependence of the dynamic susceptibility is included, then the stability of the replica-symmetric phase is enhanced.
In this paper we investigate for the infinite-range Ising spin-glass model [i.e., the Sherrington-Kirkpatrick (SK) model] with a transverse field under the static approximation by using the imaginary-time replica formalism. From the investigations we show three important results: First, we show that a replica-symmetric quantum spin-glass phase is stable in most of the area of the spin-glass phase in the temperature-transverse field phase diagram. This confirms the existence of a stable replica-symmetric spin glass phase under the static approximation, which is contrary to some previous results derived without the static approximation where the replica-symmetric solution is always unstable in the whole spin-glass phase. Second, we show our theoretical result for the nonlinear susceptibility ${\ensuremath{\chi}}_{\mathrm{nl}}$ which conforms to the experimental result of nonlinear susceptibility measurement by Wu et al. [Phys. Rev. Lett. 71, 1919 (1993)] in a quantum spin glass ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}.$ Third, in a classical (SK) spin-glass system, we confirm the anomaly in the second temperature derivative of CH/T{C}_{H}/TCH​/T near the glass transition temperature Tg,{T}_{g},Tg​, associated possibly with the field-dependent variation of entropy in the spin glass transition, which agrees with the previous experimental observation in a classical spin glass system CuMn by Fogle et al. [Phys. Rev. Lett. 50, 1815 (1983)]. We also show that this anomaly is suppressed by the nonzero transverse field of the quantum spin glass system, by which we can check for the quantum tunneling competing against spin freezing.
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.