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arXiv:cond-mat/0611168 · Journal of the Physical Society of Japan

Phase Diagram of the p-Spin-Interacting Spin Glass with Ferromagnetic Bias and a Transverse Field in the Infinite- p Limit

Tomoyuki Obuchi, Hidetoshi Nishimori, David Sherrington

Published May 11, 2007• 22 citations
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Abstract

The phase diagram of the $p$-spin-interacting spin glass model in a transverse field is investigated in the limit $p \to \infty$ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit $p \to \infty$ by using the large-$p$ expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.

DOI
10.1143/jpsj.76.054002

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The phase diagram of the ppp-spin-interacting spin glass model in a transverse field is investigated in the limit p→∞p \to \inftyp→∞ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit p→∞p \to \inftyp→∞ by using the large-ppp expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.
The authors develop systematic 1/ rho expansions for the rho -spin interaction spin-glass model in a transverse field. This model can be solved using the static approximation (SA), which is expected to be valid in the limit rho to infinity . For large, but finite rho , corrections to SA can be obtained, and the non-trivial time dependence of the imaginary time correlation function for quantum spins calculated. These corrections qualitatively change the low temperature behaviour for large rho . In particular the corrections to the SA result in the entropy vanishing exponentially as the temperature tends to zero. They compute the finite rho changes in the phase diagram, and discuss the emergence of a new critical point ending the transition line separating the two paramagnetic phases.
The Ising infinite-range spin-glass model with p-spin interactions in the presence of a transverse field is studied for large but finite p using the Matsubara time representation and Parisi's scheme of replica-symmetry breaking. In the spin-glass phase, the corrections to the limit appear much more essential than in the classical counterpart. It is shown that the quantum fluctuations have the effect of destroying the spin-glass order and a lower temperature is required to stabilize the spin-glass phase. The spin autocorrelation function in the spin-glass phase is explicitly calculated as a function of p and the Matsubara time. The result is just complementary and consistent with that previously obtained for the paramagnetic state without using the replica method.
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.