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Extremal optimization for Sherrington-Kirkpatrick spin glasses

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  • S. Boettcher

Abstract

Extremal Optimization (EO), a new local search heuristic, is used to approximate ground states of the mean-field spin glass model introduced by Sherrington and Kirkpatrick. The implementation extends the applicability of EO to systems with highly connected variables. Approximate ground states of sufficient accuracy and with statistical significance are obtained for systems with more than N=1000 variables using ±J bonds. The data reproduces the well-known Parisi solution for the average ground state energy of the model to about 0.01%, providing a high degree of confidence in the heuristic. The results support to less than 1% accuracy rational values of ω=2/3 for the finite-size correction exponent, and of ρ=3/4 for the fluctuation exponent of the ground state energies, neither one of which has been obtained analytically yet. The probability density function for ground state energies is highly skewed and identical within numerical error to the one found for Gaussian bonds. But comparison with infinite-range models of finite connectivity shows that the skewness is connectivity-dependent. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Suggested Citation

  • S. Boettcher, 2005. "Extremal optimization for Sherrington-Kirkpatrick spin glasses," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 46(4), pages 501-505, August.
    • Handle: RePEc:spr:eurphb:v:46:y:2005:i:4:p:501-505
    DOI: 10.1140/epjb/e2005-00280-6
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    Cited by:

    1. Ding, Jin & Lu, Yong-Zai & Chu, Jian, 2013. "Studies on controllability of directed networks with extremal optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6603-6615.
    2. Stefan Boettcher, 2023. "Deep reinforced learning heuristic tested on spin-glass ground states: The larger picture," Nature Communications, Nature, vol. 14(1), pages 1-3, December.
    3. Hamacher, Kay, 2007. "Energy landscape paving as a perfect optimization approach under detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 307-314.
    4. Changjun Fan & Mutian Shen & Zohar Nussinov & Zhong Liu & Yizhou Sun & Yang-Yu Liu, 2023. "Reply to: Deep reinforced learning heuristic tested on spin-glass ground states: The larger picture," Nature Communications, Nature, vol. 14(1), pages 1-4, December.
    5. Chen, Min-Rong & Lu, Yong-Zai, 2008. "A novel elitist multiobjective optimization algorithm: Multiobjective extremal optimization," European Journal of Operational Research, Elsevier, vol. 188(3), pages 637-651, August.

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