Overview
- Presents many central ideas of the mathematical theory of the Sherrington-Kirkpartrick model in detail
- Contains a fundamental breakthrough in this subject by the author
- Accessible to graduate students working in probability theory or statistical mechanics
Part of the book series: Springer Monographs in Mathematics (SMM)
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Keywords
- Aizenman-Sims-Starr scheme
- Aldous-Hoover representation
- Dovbysh-Sudakov representation
- Gaussian processes
- Ghirlanda-Guerra identities
- Guerra replica symmetry breaking
- Parisi ansatz
- Parisi formula
- Poisson processes
- Poisson-Dirichlet processes
- Ruelle probability cascades
- Sherrington-Kirkpatrick model
- Talagrand positivity principle
- exchangeability
- p-spin models
- replica symmetry breaking
- spin glass models
- ultrametricity
Table of contents (4 chapters)
Reviews
From the book reviews:
“The book is a very valuable addition to the literature in the field, and can be seen as complementary to other existing works … . I would recommend this book especially to young researchers. They can learn from it a lot about the scientific results, which could be extended to other important cases of hard optimization problems. It also provides an insight on developing original strategies when working with the difficult mathematical problems arising in studies of complex systems.” (Francesco Guerra, Bulletin of the American Mathematical Society, Vol. 52 (1), January, 2015)
“The monograph under review is concerned with the Sherrington-Kirkpatrick (SK) model of spin glasses. … The monograph deals with a notoriously difficult subject. Nevertheless, the author takes care to explain the ideas behind the proofs, which makes the text pleasant to read. It will most certainly remain a reference for years.” (José Trashorras, Mathematical Reviews, April, 2014)Authors and Affiliations
About the author
Bibliographic Information
Book Title: The Sherrington-Kirkpatrick Model
Authors: Dmitry Panchenko
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-1-4614-6289-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-6288-0Published: 21 February 2013
Softcover ISBN: 978-1-4899-9373-1Published: 06 March 2015
eBook ISBN: 978-1-4614-6289-7Published: 26 February 2013
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XII, 156
Topics: Probability Theory and Stochastic Processes, Mathematical Physics, Mathematical Methods in Physics, Complex Systems, Statistical Physics and Dynamical Systems