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

The European Physical Journal B

Dynamics of Ising spin glasses with infinite-range interactions near the de Almeida-Thouless line

Konrad H. Fischer

Published Sep 1, 1983• 12 citations
Publisher
DOI
10.1007/bf01388542

Related papers

Dynamic scaling for spin glasses near the de Almeida-Thouless line

H.-J. Sommers, Konrad H. Fischer

The European Physical Journal B•Jun 1, 1985•16 citations

The de Almeida-Thouless line of the four-dimensional Ising spin glass

Víctor Martín-Mayor

Bulletin of the American Physical Society•Mar 2, 2012•3 citations

Absence of an Almeida-Thouless line in Ising spin glasses

Helmut G. Katzgraber, A. P. Young

Bulletin of the American Physical Society•Mar 24, 2005•0 citations

de Almeida–Thouless instability in short-range Ising spin glasses

Rajiv R. P. Singh, A. P. Young

We use high-temperature series expansions to study the ±J Ising spin glass in a magnetic field in d-dimensional hypercubic lattices for d=5-8 and in the infinite-range Sherrington-Kirkpatrick (SK) model. The expansions are obtained in the variable w=tanh^{2}J/T for arbitrary values of u=tanh^{2}h/T complete to order w^{10}. We find that the scaling dimension Δ associated with the ordering-field h^{2} equals 2 in the SK model and for d≥6. However, in agreement with the work of Fisher and Sompolinsky [Phys. Rev. Lett. 54, 1063 (1985)PRLTAO0031-900710.1103/PhysRevLett.54.1063], there is a violation of scaling in a finite field, leading to an anomalous h-T dependence of the de Almeida-Thouless (AT) [J. Phys. A 11, 983 (1978)JPHAC50305-447010.1088/0305-4470/11/5/028] line in high dimensions, whereas scaling is restored as d→6. Within the convergence of our series analysis, we present evidence supporting an AT line in d≥6. In d=5, the exponents γ and Δ are substantially larger than mean-field values, but we do not see clear evidence for the AT line in d=5.

arXiv:1705.01164•Physical review. E•Jul 13, 2017•8 citations

Study of the de Almeida–Thouless Line Using Power-Law Diluted One-Dimensional Ising Spin Glasses

Helmut G. Katzgraber, Derek Larson, A. P. Young

We test for the existence of a spin-glass phase transition, the de Almeida-Thouless line, in an externally applied (random) magnetic field by performing Monte Carlo simulations on a power-law diluted one-dimensional Ising spin glass for very large system sizes. We find that a de Almeida-Thouless line occurs only in the mean-field regime, which corresponds, for a short-range spin glass, to dimension d larger than 6.

arXiv:0812.0421•Physical Review Letters•Apr 30, 2009•103 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
We use high-temperature series expansions to study the ±J Ising spin glass in a magnetic field in d-dimensional hypercubic lattices for d=5-8 and in the infinite-range Sherrington-Kirkpatrick (SK) model. The expansions are obtained in the variable w=tanh^{2}J/T for arbitrary values of u=tanh^{2}h/T complete to order w^{10}. We find that the scaling dimension Δ associated with the ordering-field h^{2} equals 2 in the SK model and for d≥6. However, in agreement with the work of Fisher and Sompolinsky [Phys. Rev. Lett. 54, 1063 (1985)PRLTAO0031-900710.1103/PhysRevLett.54.1063], there is a violation of scaling in a finite field, leading to an anomalous h-T dependence of the de Almeida-Thouless (AT) [J. Phys. A 11, 983 (1978)JPHAC50305-447010.1088/0305-4470/11/5/028] line in high dimensions, whereas scaling is restored as d→6. Within the convergence of our series analysis, we present evidence supporting an AT line in d≥6. In d=5, the exponents γ and Δ are substantially larger than mean-field values, but we do not see clear evidence for the AT line in d=5.
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).