The correspondence between long-range and short-range spin glasses

Abstract

We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power sigma of the distance. We show that there is a value of sigma of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions. We also study a value of sigma for which we find the critical behavior to be compatible with that of the three dimensional model, though we have much less precision than in the four-dimensional case.

15 pages, 10 figures

References in corpus (9)

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Cited by in corpus (8)

• Spin glasses in a field: Three and four dimensions as seen from one space dimension
• The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority
• Testing statics-dynamics equivalence at the spin-glass transition in three dimensions
• The Ising Spin Glass in dimension four
• Infinite volume extrapolation in the one-dimensional bond diluted Levy spin-glass model near its lower critical dimension
• Evidence for non-universal scaling in dimension four Ising spin glasses
• Spin glass behavior in a random Coulomb antiferromagnet
• Statistical mechanics of the spherical hierarchical model with random fields