Analytic theory of the ground state properties of a spin glass. I. Ising spin glass
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A general theory to count the number of local minimum states in an Ising spin glass is developed. The problem is reduced to finding the partition function of an interacting non-random spin system with an imaginary spin weight function. For the infinite-ranged spin glass with Gaussian bond distribution, the authors find (g 0 )=2 0.28743N for the average number of the local minimum states. The distribution function for the energies of these states is also studied. The upper limit of the average ground state energy per spin of the infinite-ranged spin glass is found to be -J/ square root 2 pi .
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The number of energy minima (spurious states, stable states) of Hopfield networks is exponentially in d.
“In contrast to the storage capacity, the number of energy minima (spurious states, stable states) of Hopfield networks is exponentially in d (Tanaka & Edwards, 1980; Bruck & Roychowdhury, 1990; Wainrib & Touboul, 2013).”
From Hopfield Networks is All You Need (2020) · cites this paper as Tanaka & Edwards, 1980
Section 4, “Infinite-ranged spin glass,” gives an exponential-in-N count of local minimum states for an Ising spin glass, where N is the number of spins. It does not establish that count for Hopfield networks specifically, so the claim extends the result beyond the model studied. (LLM, conf=0.88)
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Hopfield Networks is All You Need
Ramsauer, H., Schäfl, B., Lehner, J., Seidl, P., Widrich, M., Adler, T., Gruber, L., Holzleitner, M., Pavlović, M., Sandve, G. K., et al. (2020) · arXiv · doi:10.48550/arxiv.2008.02217 · Cited by 236 · see citing works
- Authors
- Tanaka, F., & Edwards, S. F.
- Affiliations
- University of Cambridge (GB)
- Venue
- Journal of Physics F: Metal Physics
- Publisher
- IOP Publishing
- Published
- 1980-12
- Volume
- 10
- Issue
- 12
- Pages
- 2769-2778
- ISSN
- 0305-4608 (ISSN-L)
- OpenAlex
- W2059775469
- Cited by
- 127
- References
- 0
- Citations by year
- 2025: 1 · 2024: 2 · 2023: 1 · 2022: 1 · 2021: 3 · 2020: 6 · 2019: 6 · 2018: 5 · 2017: 5 · 2016: 2 · 2015: 2 · 2014: 1 · 2013: 1 · 2012: 3
- FWCI
- 2.35
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics F Metal Physics (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 › Mathematical Physics › advanced mathematical theories
- Keywords
- Ising spin glass, ground-state properties, partition function, energy distribution
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