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arXiv · 0803.3417

New Insights from One-Dimensional Spin Glasses

Helmut G. Katzgraber·Alexander K. Hartmann·A. P. Young
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Abstract

The 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.

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Helmut G. Katzgraber, Alexander K. Hartmann, A. P. Young. 2008-03-24. New Insights from One-Dimensional Spin Glasses. https://arxiv.org/abs/0803.3417

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