New Insights from One-Dimensional Spin Glasses

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dc.creatorKatzgraber, Helmut G.
dc.creatorHartmann, Alexander K.
dc.creatorYoung, A. P.
dc.date2008-03-24
dc.date.accessioned2026-07-07T09:28:07Z
dc.date.available2026-07-07T09:28:07Z
dc.descriptionThe concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial analysis. Thus it is of paramount importance to understand which predictions of the mean-field solution apply to non-mean-field systems, such as realistic short-range spin-glass models. The one-dimensional spin glass with random power-law interactions promises to be an ideal test-bed to answer this question: Not only can large system sizes-which are usually a shortcoming in simulations of high-dimensional short-range system-be studied, by tuning the power-law exponent of the interactions the universality class of the model can be continuously tuned from the mean-field to the short-range universality class. We present details of the model, as well as recent applications to some questions of the physics of spin glasses. First, we study the existence of a spin-glass state in an external field. In addition, we discuss the existence of ultrametricity in short-range spin glasses. Finally, because the range of interactions can be changed, the model is a formidable test-bed for optimization algorithms.
dc.description15 pages, 8 figures. To appear in: Computer Simulation Studies in Condensed Matter Physics XXI, Eds. D.P. Landau, S.P. Lewis, and H.B. Schuttler (Springer Verlag, Heidelberg, Berlin 2008)
dc.identifierhttps://arxiv.org/abs/0803.3417
dc.identifierhttp://arxiv.org/abs/0803.3417
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157341
dc.subjectDisordered Systems and Neural Networks
dc.titleNew Insights from One-Dimensional Spin Glasses
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