### Abstract

The spectrum of the stability matrix associated with Sompolinsky's solution (1981) for a long-range spin glass is studied near T_{c} 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 language | English |
---|---|

Article number | 005 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 16 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1983 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*16*(2), [005]. https://doi.org/10.1088/0305-4470/16/2/005

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 16, no. 2, 005. https://doi.org/10.1088/0305-4470/16/2/005

}

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 -