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Spin Glasses and Complexity$
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Daniel L. Stein and Charles M. Newman

Print publication date: 2013

Print ISBN-13: 9780691147338

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691147338.001.0001

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Short-Range Spin Glasses: Some Basic Questions

Short-Range Spin Glasses: Some Basic Questions

(p.175) 7 Short-Range Spin Glasses: Some Basic Questions
Spin Glasses and Complexity

Daniel L. Stein

Charles M. Newman

Princeton University Press

This chapter discusses short-range spin glasses. It considers realistic spin glass models, in particular the Edwards–Anderson (EA) model. Both the EA and the Sherrington–Kirkpatrick (SK) models are idealizations of the complicated spatial structure of spin–spin interactions in real materials. In the EA idealization, the interactions are extremely short range, occurring only between spins that are nearest neighbors in the atomic lattice. This caricatures the actual spatial structure of laboratory spin glasses, but the EA model is nevertheless believed to distill their essential physics. In contrast, the SK model is bereft of geometric structure and behaves like an EA model in the limit of infinite dimension. Since we are really interested in finite dimensions, it is important to understand not only how the phenomena exhibited by the EA model depend on dimension d, but also how the similarities and differences between the EA and SK models depend on dimension.

Keywords:   spin glasses, Edwards–Anderson model, Sherrington–Kirkpatrick model, dimension, spin–spin interaction

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