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Journal of Physics Condensed Matter

Transverse freezing in the infinite-range quantum Ising spin glass with transverse and Gaussian random longitudinal fields

Yu‐qiang Ma, Zhen‐Ya Li, Chang-De Gong

Published Jun 24, 1991• 9 citations
Publisher

Abstract

The infinite-range quantum Ising spin glass in a transverse and a Gaussian random field has been studied by combining the pair approximation with the discretized path-integral representation. The phase diagrams are obtained, and the possibilities of the existence of a mixed phase in which ferromagnetism and spin-glass order coexist are discussed. This is expected to interpret some properties of the mixed hydrogen-bonded ferroelectric and antiferroelectric crystals such as Rb 1-x (NH) 4x H 2 PO.

DOI
10.1088/0953-8984/3/25/015

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The infinite-range quantum Ising spin glass in a transverse and a Gaussian random field has been studied by combining the pair approximation with the discretized path-integral representation. The phase diagrams are obtained, and the possibilities of the existence of a mixed phase in which ferromagnetism and spin-glass order coexist are discussed. This is expected to interpret some properties of the mixed hydrogen-bonded ferroelectric and antiferroelectric crystals such as Rb 1-x (NH) 4x H 2 PO.
The infinite-range quantum Heisenberg spin glass with uniaxial anisotropy (D) and coaxial external magnetic field (h) is studied by means of the thermo-field-dynamics as a substitute for the n-replica trick. Within the mean-field theory a multiplicity of spin-glass phases has been found for the spin values S=1 and S=3/2, respectively, including: longitudinal, transverse, and mixed phases. The stability of the mean-field-type solution against the action of fluctuations has been investigated and the existence of a crossover from the longitudinal-to-transverse freezing is demonstrated explicitly in the temperature-field (T-h) phase diagram for various values of the constant D.
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 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.