Perspectives on Spin Glasses

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Mathematics
Cover of the book Perspectives on Spin Glasses by Pierluigi Contucci, Cristian Giardinà, Cambridge University Press
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Author: Pierluigi Contucci, Cristian Giardinà ISBN: 9781139793292
Publisher: Cambridge University Press Publication: October 18, 2012
Imprint: Cambridge University Press Language: English
Author: Pierluigi Contucci, Cristian Giardinà
ISBN: 9781139793292
Publisher: Cambridge University Press
Publication: October 18, 2012
Imprint: Cambridge University Press
Language: English

Presenting and developing the theory of spin glasses as a prototype for complex systems, this book is a rigorous and up-to-date introduction to their properties. The book combines a mathematical description with a physical insight of spin glass models. Topics covered include the physical origins of those models and their treatment with replica theory; mathematical properties like correlation inequalities and their use in the thermodynamic limit theory; main exact solutions of the mean field models and their probabilistic structures; and the theory of the structural properties of the spin glass phase such as stochastic stability and the overlap identities. Finally, a detailed account is given of the recent numerical simulation results and properties, including overlap equivalence, ultrametricity and decay of correlations. The book is ideal for mathematical physicists and probabilists working in disordered systems.

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Presenting and developing the theory of spin glasses as a prototype for complex systems, this book is a rigorous and up-to-date introduction to their properties. The book combines a mathematical description with a physical insight of spin glass models. Topics covered include the physical origins of those models and their treatment with replica theory; mathematical properties like correlation inequalities and their use in the thermodynamic limit theory; main exact solutions of the mean field models and their probabilistic structures; and the theory of the structural properties of the spin glass phase such as stochastic stability and the overlap identities. Finally, a detailed account is given of the recent numerical simulation results and properties, including overlap equivalence, ultrametricity and decay of correlations. The book is ideal for mathematical physicists and probabilists working in disordered systems.

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