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Cluster-exact approximation of spin glass groundstates

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  • Hartmann, Alexander K.

Abstract

We present a fast (∼ O (N3)) algorithm which calculates groundstates of Ising spin glasses approximately. It works by randomly selecting clusters of spins which exhibit no frustrations. The spins which were not selected, contribute to the local fields of the selected spins. For the spin-cluster a groundstate is exactly calculated by using graphtheoretical methods. The other spins remain unchanged. This procedure is repeated many times resulting in a state of low energy. The total time complexity of this scheme is approximately cubic. To demonstrate how deep in energy this algorithm can get, we applied it to the ±J model. We estimate that the groundstate energy density of the infinite system is −1.400 ± 0.005 (2d) and −1.766 ± 0.002 (3d). Finally the distribution of overlaps for selected systems is calculated in order to characterize the algorithm.

Suggested Citation

  • Hartmann, Alexander K., 1996. "Cluster-exact approximation of spin glass groundstates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 224(3), pages 480-488.
    • Handle: RePEc:eee:phsmap:v:224:y:1996:i:3:p:480-488
    DOI: 10.1016/0378-4371(95)00404-1
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    References listed on IDEAS

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    1. L. R. Ford, Jr. & D. R. Fulkerson, 1956. "Solving the Transportation Problem," Management Science, INFORMS, vol. 3(1), pages 24-32, October.
    2. Maurice Queyranne, 1980. "Theoretical Efficiency of the Algorithm “Capacity” for the Maximum Flow Problem," Mathematics of Operations Research, INFORMS, vol. 5(2), pages 258-266, May.
    3. Hartmann, A.K. & Usadel, K.D., 1995. "Exact determination of all ground states of random field systems in polynomial time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(2), pages 141-152.
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