### Abstract

Parisi's replica symmetry breaking solution for spin glasses is extended to finite replica number n. The free energy F_{p}(n) obtained this way, as well as its first two derivatives with respect to n, are shown to join the corresponding values in the Sherrington-Kirkpatrick (SK) solution at a characteristic value n_{s}(T), where stability breaks down in the latter. The continuation composed of the SK branch F_{SK}(n) for n>or=n_{s}(T) and the Parisi branch F_{P}(n) for 0S(T) fulfils the requirements of convexity, monotonicity and stability for all n.

Original language | English |
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Article number | 006 |

Journal | Journal of Physics A: General Physics |

Volume | 16 |

Issue number | 4 |

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

**Parisi's mean-field solution for spin glasses as an analytic continuation in the replica number.** / Kondor, I.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Parisi's mean-field solution for spin glasses as an analytic continuation in the replica number

AU - Kondor, I.

PY - 1983

Y1 - 1983

N2 - Parisi's replica symmetry breaking solution for spin glasses is extended to finite replica number n. The free energy Fp(n) obtained this way, as well as its first two derivatives with respect to n, are shown to join the corresponding values in the Sherrington-Kirkpatrick (SK) solution at a characteristic value ns(T), where stability breaks down in the latter. The continuation composed of the SK branch FSK(n) for n>or=ns(T) and the Parisi branch FP(n) for 0S(T) fulfils the requirements of convexity, monotonicity and stability for all n.

AB - Parisi's replica symmetry breaking solution for spin glasses is extended to finite replica number n. The free energy Fp(n) obtained this way, as well as its first two derivatives with respect to n, are shown to join the corresponding values in the Sherrington-Kirkpatrick (SK) solution at a characteristic value ns(T), where stability breaks down in the latter. The continuation composed of the SK branch FSK(n) for n>or=ns(T) and the Parisi branch FP(n) for 0S(T) fulfils the requirements of convexity, monotonicity and stability for all n.

UR - http://www.scopus.com/inward/record.url?scp=0001418032&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001418032&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/16/4/006

DO - 10.1088/0305-4470/16/4/006

M3 - Article

AN - SCOPUS:0001418032

VL - 16

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 4

M1 - 006

ER -