Abstract
In this chapter we introduce the basic concepts and methods through the study of the Sherrington-Kirkpatrick model with external field, the archetypical model for spin glasses. We develop in particular the cavity method, which is basically induction over the number of spins, and that is a major theme through this entire work. We describe very precisely the behavior of the model at high enough temperature. We then briefly examine multi-dimensional versions of this model. In subsequent chapters we examine a number of different models, each of which presents at least a strikingly different new feature.
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© 2011 Springer-Verlag Berlin Heidelberg
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Talagrand, M. (2011). The Sherrington-Kirkpatrick Model. In: Mean Field Models for Spin Glasses. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15202-3_1
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DOI: https://doi.org/10.1007/978-3-642-15202-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15201-6
Online ISBN: 978-3-642-15202-3
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