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Comparative monte Carlo study of ising spin glasses in two to five dimensions

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Zeitschrift für Physik B Condensed Matter

Abstract

Monte Carlo simulations of the Edwards-Anderson-Ising spin glass with Gaussian distribution of nearest-neighbor exchange forces in four and five dimensions are performed to check the speculation thatd=4 is the lower critical dimensionality. In contrast to this expectation we find no qualitative difference at all to the results in two and three dimensions. We still find that on not too long time-scales there is an apparently rather well defined freezing temperatureT f , where the susceptibility has a cusp, and belowT f nonzero order parametersq, ψ can be found as ford=2, 3. But even ford=5 the decay of the Edwards-Anderson order parameter belowT f is found to be consistent with a logarithmic variation over several decades of observation time. The possible interpretations of this result are discussed. Our data thus suggest that either there is no equilibrium phase transition in all these dimensions, or more likely that a phase transition exists for 2≦d≦5 but the properties of the ‘ordered phase’ may be rather peculiar.

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Authors and Affiliations

  1. Institut für Festkörperforschung, Kernforschungsanlage Jülich GmbH, Postfach 1913, D-5170, Jülich 1, Germany

    K. Binder

  2. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, D-5000, Köln 41, Germany

    D. Stauffer

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  1. D. Stauffer
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  2. K. Binder
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Sonderforschungsbereich 125 Aachen-Jülich-Köln

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Stauffer, D., Binder, K. Comparative monte Carlo study of ising spin glasses in two to five dimensions. Z Physik B 34, 97–105 (1979). https://doi.org/10.1007/BF01362783

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  • DOI: https://doi.org/10.1007/BF01362783

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