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Exact ground states of two-dimensional ±J Ising spin glasses

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Abstract

In this paper we study the problem of finding an exact ground state of a two-dimensional ±J Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is a concentrationp of negative bonds, withp ranging between 0.1 and 0.9. With our exact algorithm we can determine ground states of grids of sizes up to 50×50 in a moderate amount of computation time (up to 1 hr each) for several values ofp. For the ground-state energy of an infinite spin-glass system withp=0.5 we estimateE ∞0.5 =−1.4015±0.0008. We report on extensive computational tests based on more than 22,000 experiments.

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Author notes

  1. C. De Simone

    Present address: IASI-CNR, 00185, Rome, Italy

Authors and Affiliations

  1. Institut für Informatik, Universität zu Köln, 50969, Köln, Germany

    C. De Simone, M. Diehl & M. Jünger

  2. IASI-CNR, 00185, Rome, Italy

    G. Rinaldi

  3. MPI für Informatik, 66123, Saarbrücken, Germany

    P. Mutzel

  4. Institut für Angewandte Mathematik, Universität Heidelberg, 69120, Heidelberg, Germany

    G. Reinelt

Authors
  1. C. De Simone
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  2. M. Diehl
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  3. M. Jünger
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  4. P. Mutzel
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  5. G. Reinelt
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  6. G. Rinaldi
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De Simone, C., Diehl, M., Jünger, M. et al. Exact ground states of two-dimensional ±J Ising spin glasses. J Stat Phys 84, 1363–1371 (1996). https://doi.org/10.1007/BF02174135

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  • DOI: https://doi.org/10.1007/BF02174135

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