Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Phase diagram of the quantum Ising spin glass in a transverse field

Klaus D. Usadel, G. Büttner, T. K. Kopeć

Published Dec 1, 1991• 22 citations
Publisher

Abstract

A recent calculation of Yokota on the phase boundary for the Sherrington-Kirkpatrick version of the quantum Ising spin glass in a transverse field seems to lead to unphysical results. Various other approaches on this subject are quoted and compared with the exact Trotter-Suzuki method to resolve the controversies about the critical line in this model.

DOI
10.1103/physrevb.44.12583

Related papers

Monte Carlo Studies of the Ising Spin-Glass in a Transverse Field

Pik-Yin Lai, Yadin Y. Goldschmidt

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.

Europhysics Letters (EPL)•Oct 15, 1990•19 citations

Ising spin glass in a transverse magnetic field

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

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.

arXiv:cond-mat/9312036•Physical review. B, Condensed matter•Mar 1, 1994•25 citations

Correlations in the Trotter dimension in the transverse Ising spin-glass model

Ferenc Pázmándi, Zbigniew Domański, Paul Erdös

The nature of the paramagnetic phase of the transverse Sherrington-Kirkpatrick (SK) spin-glass model is not completely understood because of the quantum fluctuations. We use different approximations to describe these fluctuations. The resulting paramagnetic--spin-glass phase diagrams are compared to those obtained by numerical methods and by previous theories.

Physical review. B, Condensed matter•Apr 1, 1993•7 citations

Phase diagrams of the quantum Sherrington-Kirkpatrick Ising spin glass in a transverse field

Yu‐qiang Ma, Zhen‐Ya Li

Physics Letters A•Aug 1, 1990•13 citations

Sherrington-Kirkpatrick model in a transverse field: Absence of replica symmetry breaking due to quantum fluctuations

Purusattam Ray, Bikas K. Chakrabarti, Arunava Chakrabarti

The Sherrington-Kirkpatrick model under a transverse field is studied here employing the Suzuki-Trotter formula to map the model to an equivalent classical one. The effective Thouless-Anderson-Palmer free energy is used to study the stability of the system, and Monte Carlo computer simulations of the effective classical model are performed to obtain the phase diagram and the magnetization overlap distribution. Our results indicate a trivial overlap distribution due to quantum fluctuations. The phase diagram shows a slight initial increase in the glass transition temperature ${T}_{g}$ as the transverse field is switched on, confirming that obtained by Yokota.

Physical review. B, Condensed matter•Jun 1, 1989•208 citations

Stability of the quantum Sherrington-Kirkpatrick spin glass model

A. P. Young

I study in detail the quantum Sherrington-Kirkpatrick (SK) model, i.e., the infinite-range Ising spin glass in a transverse field, by solving numerically the effective one-dimensional model that the quantum SK model can be mapped to in the thermodynamic limit. I find that the replica symmetric solution is unstable down to zero temperature, in contrast to some previous claims, and so there is not only a line of transitions in the (longitudinal) field-temperature plane (the de Almeida-Thouless, AT, line) where replica symmetry is broken, but also a quantum de Almeida-Thouless (QuAT) line in the transverse field-longitudinal field plane at T=0. If the QuAT line also occurs in models with short-range interactions its presence might affect the performance of quantum annealers when solving spin glass-type problems with a bias (i.e., magnetic field).

arXiv:1707.07107•Physical review. E•Sep 11, 2017•29 citations
A recent calculation of Yokota on the phase boundary for the Sherrington-Kirkpatrick version of the quantum Ising spin glass in a transverse field seems to lead to unphysical results. Various other approaches on this subject are quoted and compared with the exact Trotter-Suzuki method to resolve the controversies about the critical line in this model.
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.
The Sherrington-Kirkpatrick model under a transverse field is studied here employing the Suzuki-Trotter formula to map the model to an equivalent classical one. The effective Thouless-Anderson-Palmer free energy is used to study the stability of the system, and Monte Carlo computer simulations of the effective classical model are performed to obtain the phase diagram and the magnetization overlap distribution. Our results indicate a trivial overlap distribution due to quantum fluctuations. The phase diagram shows a slight initial increase in the glass transition temperature Tg{T}_{g}Tg​ as the transverse field is switched on, confirming that obtained by Yokota.
I study in detail the quantum Sherrington-Kirkpatrick (SK) model, i.e., the infinite-range Ising spin glass in a transverse field, by solving numerically the effective one-dimensional model that the quantum SK model can be mapped to in the thermodynamic limit. I find that the replica symmetric solution is unstable down to zero temperature, in contrast to some previous claims, and so there is not only a line of transitions in the (longitudinal) field-temperature plane (the de Almeida-Thouless, AT, line) where replica symmetry is broken, but also a quantum de Almeida-Thouless (QuAT) line in the transverse field-longitudinal field plane at T=0. If the QuAT line also occurs in models with short-range interactions its presence might affect the performance of quantum annealers when solving spin glass-type problems with a bias (i.e., magnetic field).