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Finding Low-Temperature States With Parallel Tempering, Simulated Annealing And Simple Monte Carlo

Author

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  • J. J. MORENO

    (Department of Physics, University of California Davis, Davis, CA 95616, USA)

  • HELMUT G. KATZGRABER

    (Department of Physics, University of California Davis, Davis, CA 95616, USA)

  • ALEXANDER K. HARTMANN

    (Institut für Theoretische Physik, Universität Göttingen, Bunsenstr. 9, D-37073 Göttingen, Germany)

Abstract

Monte Carlo simulation techniques, like simulated annealing and parallel tempering, are often used to evaluate low-temperature properties and find ground states of disordered systems. Here we compare these methods using direct calculations of ground states for three-dimensional Ising diluted antiferromagnets in a field (DAFF) and three-dimensional Ising spin glasses (ISG). For the DAFF, we find that, with respect to obtaining ground states, parallel tempering is superior to simple Monte Carlo and to simulated annealing. However, equilibration becomes more difficult with increasing magnitude of the externally applied field. For the ISG with bimodal couplings, which exhibits a high degeneracy, we conclude that finding true ground states is easy for small systems, as is already known. But finding each of the degenerate ground states with the same probability (or frequency), as required by Boltzmann statistics, is considerably harder and becomes almost impossible for larger systems.

Suggested Citation

  • J. J. Moreno & Helmut G. Katzgraber & Alexander K. Hartmann, 2003. "Finding Low-Temperature States With Parallel Tempering, Simulated Annealing And Simple Monte Carlo," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 285-302.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:03:n:s0129183103004498
    DOI: 10.1142/S0129183103004498
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    References listed on IDEAS

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    1. Parisi, Giorgio, 1986. "Spin glasses theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 140(1), pages 312-318.
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    Cited by:

    1. Max Bodenstein & Ingo Liere-Netheler & Frank Schuldt & Karsten von Maydell & Alexander K. Hartmann & Carsten Agert, 2023. "Optimized Power Flow Control to Minimize Congestion in a Modern Power System," Energies, MDPI, vol. 16(12), pages 1-19, June.

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