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The ground state energy of the Edwards–Anderson spin glass model with a parallel tempering Monte Carlo algorithm

Author

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  • Romá, F.
  • Risau-Gusman, S.
  • Ramirez-Pastor, A.J.
  • Nieto, F.
  • Vogel, E.E.

Abstract

We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards–Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two- and three-dimensional lattices. By a systematic analysis we find a simple formula to estimate the values of the parameters needed in the algorithm to find the GS with a fixed average probability. We also study the performance of the algorithm for single samples, quantifying the difference between samples where the GS is hard, or easy, to find. The GS energies we obtain are in good agreement with the values found in the literature. Our results show that the performance of the parallel tempering technique is comparable to more powerful heuristics developed to find the ground state of Ising spin glass systems.

Suggested Citation

  • Romá, F. & Risau-Gusman, S. & Ramirez-Pastor, A.J. & Nieto, F. & Vogel, E.E., 2009. "The ground state energy of the Edwards–Anderson spin glass model with a parallel tempering Monte Carlo algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2821-2838.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:14:p:2821-2838
    DOI: 10.1016/j.physa.2009.03.036
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    Cited by:

    1. 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.

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