The spectrum of fluctuations around Sompolinsky's mean field solution for a spin glass

I. Kondor, C. De Dominicis

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The spectrum of the stability matrix associated with Sompolinsky's solution (1981) for a long-range spin glass is studied near Tc in a magnetic field. It is shown that the reparametrisation (or gauge) invariance of the theory locks together not only the order parameters q(x) and Delta (x) but also their fluctuations, and gives rise to a gauge-invariant spectrum which is therefore the same both for the Parisi solution (1979) and for the Sompolinsky solution. In the limit of zero magnetic field, earlier results for the Parisi solution are recovered. The marginal stability of both theories is demonstrated for all fields in the Almeida-Thouless phase.

Original languageEnglish
Article number005
JournalJournal of Physics A: Mathematical and General
Volume16
Issue number2
DOIs
Publication statusPublished - 1983

Fingerprint

Spin glass
Spin Glass
Mean Field
spin glass
Magnetic Field
Fluctuations
Reparametrization
Gauge Invariance
Order Parameter
Gages
Gauge
Magnetic fields
Invariant
gauge invariance
Zero
Stiffness matrix
Invariance
magnetic fields
Range of data
matrices

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

The spectrum of fluctuations around Sompolinsky's mean field solution for a spin glass. / Kondor, I.; De Dominicis, C.

In: Journal of Physics A: Mathematical and General, Vol. 16, No. 2, 005, 1983.

Research output: Contribution to journalArticle

@article{66c8a0c613e34a5e8daac48df273c7dc,
title = "The spectrum of fluctuations around Sompolinsky's mean field solution for a spin glass",
abstract = "The spectrum of the stability matrix associated with Sompolinsky's solution (1981) for a long-range spin glass is studied near Tc in a magnetic field. It is shown that the reparametrisation (or gauge) invariance of the theory locks together not only the order parameters q(x) and Delta (x) but also their fluctuations, and gives rise to a gauge-invariant spectrum which is therefore the same both for the Parisi solution (1979) and for the Sompolinsky solution. In the limit of zero magnetic field, earlier results for the Parisi solution are recovered. The marginal stability of both theories is demonstrated for all fields in the Almeida-Thouless phase.",
author = "I. Kondor and {De Dominicis}, C.",
year = "1983",
doi = "10.1088/0305-4470/16/2/005",
language = "English",
volume = "16",
journal = "Journal Physics D: Applied Physics",
issn = "0022-3727",
publisher = "IOP Publishing Ltd.",
number = "2",

}

TY - JOUR

T1 - The spectrum of fluctuations around Sompolinsky's mean field solution for a spin glass

AU - Kondor, I.

AU - De Dominicis, C.

PY - 1983

Y1 - 1983

N2 - The spectrum of the stability matrix associated with Sompolinsky's solution (1981) for a long-range spin glass is studied near Tc in a magnetic field. It is shown that the reparametrisation (or gauge) invariance of the theory locks together not only the order parameters q(x) and Delta (x) but also their fluctuations, and gives rise to a gauge-invariant spectrum which is therefore the same both for the Parisi solution (1979) and for the Sompolinsky solution. In the limit of zero magnetic field, earlier results for the Parisi solution are recovered. The marginal stability of both theories is demonstrated for all fields in the Almeida-Thouless phase.

AB - The spectrum of the stability matrix associated with Sompolinsky's solution (1981) for a long-range spin glass is studied near Tc in a magnetic field. It is shown that the reparametrisation (or gauge) invariance of the theory locks together not only the order parameters q(x) and Delta (x) but also their fluctuations, and gives rise to a gauge-invariant spectrum which is therefore the same both for the Parisi solution (1979) and for the Sompolinsky solution. In the limit of zero magnetic field, earlier results for the Parisi solution are recovered. The marginal stability of both theories is demonstrated for all fields in the Almeida-Thouless phase.

UR - http://www.scopus.com/inward/record.url?scp=4744353910&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4744353910&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/16/2/005

DO - 10.1088/0305-4470/16/2/005

M3 - Article

AN - SCOPUS:4744353910

VL - 16

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 2

M1 - 005

ER -