Correspondence between long-range and short-range spin glasses

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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.
© 2012 American Physical Society. We thank G. Parisi and M. Moore for discussions. A.P.Y. acknowledges support from the NSF through Grant No. DMR- 0906366 and a generous allocation of computer time from the Hierarchical Systems Research Foundation. The shortrange simulations, and part of the long-range simulations, were carried out on ARAGRID and BIFI computers. R.A.B., L.A.F., and V.M.M. acknowledge partial financial support from MICINN, Spain, Contract No. FIS2009 12648-C03. R.A.B. was also supported by the FPI Program (Diputación de Aragón, Spain). V.M.M. acknowledges the hospitality of the Physics Department of UCSC (visit funded by the Del Amo Foundation), where part of this work was performed.
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