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Improved extremal optimization for the Ising spin glass.

A Alan Middleton1

  • 1Department of Physics, Syracuse University, Syracuse, New York 13244, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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This study introduces an adaptive extremal optimization (EO) algorithm that significantly accelerates finding ground states in spin glasses. The enhanced heuristic offers substantial speedups for materials with quenched disorder.

Area of Science:

  • Condensed matter physics
  • Computational physics
  • Statistical mechanics

Background:

  • Spin glasses are complex magnetic materials with quenched disorder.
  • Extremal optimization (EO) is a heuristic algorithm used for finding ground states.
  • Existing EO algorithms can be computationally intensive for large systems.

Purpose of the Study:

  • To introduce and test a modified extremal optimization (EO) algorithm.
  • To improve the efficiency of finding exact ground states in spin glass models.
  • To assess the performance of the adaptive algorithm for materials with quenched disorder.

Main Methods:

  • The study implements a variant of the extremal optimization (EO) algorithm.
  • This adaptive algorithm reduces the probability of re-flipping selected spins.

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  • The algorithm is tested on two- and three-dimensional spin glass models with Gaussian disorder.

    • Main Results:

    • The adaptive EO algorithm demonstrates significant speedups compared to the original EO.
    • Speedups of 10^4 and 10^2 were observed for 16^2- and 8^3-spin samples, respectively.
    • The observed speedup increases rapidly with increasing system size.

    Conclusions:

    • The adaptive extremal optimization (EO) algorithm is a highly efficient heuristic.
    • This method offers a valuable tool for studying materials with quenched disorder.
    • The algorithm's performance suggests potential applications in materials science and complex systems analysis.