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

de Almeida–Thouless instability in short-range Ising spin glasses 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=tanh2J/T for arbitrary values of u=tanh2h/T complete to order w10. We find that the scaling dimension Δ associated with the ordering-field h2 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review E American Physical Society (APS)

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

Preview Only

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

Abstract

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=tanh2J/T for arbitrary values of u=tanh2h/T complete to order w10. We find that the scaling dimension Δ associated with the ordering-field h2 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.
Loading next page...
 
/lp/aps_physical/de-almeida-thouless-instability-in-short-range-ising-spin-glasses-p3vI2wBeJ0
Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1539-3755
eISSN
550-2376
D.O.I.
10.1103/PhysRevE.96.012127
Publisher site
See Article on Publisher Site

Abstract

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=tanh2J/T for arbitrary values of u=tanh2h/T complete to order w10. We find that the scaling dimension Δ associated with the ordering-field h2 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.

Journal

Physical Review EAmerican Physical Society (APS)

Published: Jul 13, 2017

There are no references for this article.

Sorry, we don’t have permission to share this article on DeepDyve,
but here are related articles that you can start reading right now:

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial