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Ground States For Large Samples Of Two-Dimensional Ising Spin Glasses

Author

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  • R. G. PALMER

    (Department of Physics, Duke University, Durham, NC, 27708-0305, USA)

  • JOAN ADLER

    (Department of Physics, Duke University, Durham, NC, 27708-0305, USA;
    Department of Physics, Technion Haifa, 32000, Israel)

Abstract

We have developed a combinatoric matching method to find the exact groundstate energy for the 2-D Ising spin glass with the± Jdistribution and equal numbers of positive and negative bonds. For the largest size (1800×1800plaquettes of spins), we averaged results from 278 samples and for the smaller ones up to 374, 375 samples. We also studied the behavior of the distributions of computer time (CPU) and memory as functions of sample size. We present finite size scaling leading to a groundstate energy estimate ofE∞=-1.40193±2for the infinite system. We found that the memory scales as the square of sample length and that for a given size, the CPU time appears to have a skewed and high-tailed distribution.

Suggested Citation

  • R. G. Palmer & Joan Adler, 1999. "Ground States For Large Samples Of Two-Dimensional Ising Spin Glasses," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 667-675.
    • Handle: RePEc:wsi:ijmpcx:v:10:y:1999:i:04:n:s0129183199000504
    DOI: 10.1142/S0129183199000504
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    Cited by:

    1. F. Liers & G. Pardella, 2012. "Partitioning planar graphs: a fast combinatorial approach for max-cut," Computational Optimization and Applications, Springer, vol. 51(1), pages 323-344, January.

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