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This research compares critical behavior in long-range and short-range spin glasses, revealing similarities and implications.
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 σ of the distance. We show that there is a value of σ 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 σ for which we find the critical behavior to be compatible with that of the three-dimensional model, although we have much less precision than in the four-dimensional case.
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Baños et al. (2012) studied this question.
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