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Parisi's mean-field solution for spin glasses as an analytic continuation in the replica number
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 0<or=n<or=n S (T) fulfils the requirements of convexity, monotonicity and stability for all n.
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“The correct analytic continuation to m ¼ 0 will then be determined by the behavior of the ansatz for q ðα;γÞ which remains stable down to m ¼ 0; this behavior will undergo a phase transition at some critical m c ðTÞ < 1 [69] that was missed by just considering the replica-symmetric ansatz (5.9).”
From Free energy from replica wormholes (2021) · cites this paper as [69]
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Research works printed but not linked: 15
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Cited by
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Free energy from replica wormholes
Engelhardt, N., Fischetti, S., & Maloney, A. (2021) · Physical Review D · doi:10.1103/physrevd.103.046021 · Cited by 90
Metadata
- Authors
- Kondor, I.
- Affiliations
- Eötvös Loránd University (HU)
- Corresponding author
- Kondor, I
- ORCID
- Kondor, I
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1983-03-11
- Volume
- 16
- Issue
- 4
- Pages
- L127-L131
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2022737266
- Cited by
- 128
- References
- 0
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2021: 2 · 2019: 4 · 2017: 1 · 2015: 1 · 2014: 2 · 2012: 1
- FWCI
- 9.57
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Materials Science › Materials Chemistry › Material Dynamics and Properties
- Physical Sciences › Mathematics › Statistics and Probability › Random Matrices and Applications
- Keywords
- Parisi solution, replica symmetry breaking, spin glass, analytic continuation, Sherrington-Kirkpatrick model, free energy, mean-field theory
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- The paper
- Kondor, I. (1983). Parisi's mean-field solution for spin glasses as an analytic continuation in the replica number. Journal of Physics A: Mathematical and General. https://doi.org/10.1088/0305-4470/16/4/006
