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

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Abstract

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.

Original languageEnglish
Article number006
JournalJournal of Physics A: General Physics
Volume16
Issue number4
DOIs
Publication statusPublished - 1983

Fingerprint

Spin glass
Analytic Continuation
Spin Glass
Replica
replicas
Mean Field
spin glass
Branch
convexity
Frequency shift keying
Symmetry Breaking
Free energy
Continuation
Join
Breakdown
Monotonicity
Convexity
Free Energy
broken symmetry
breakdown

ASJC Scopus subject areas

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

Cite this

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abstract = "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.",
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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.

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