Springer Monographs in Mathematics

The Sherrington-Kirkpatrick Model

Authors: Panchenko, Dmitry

  • ​​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
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eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-6289-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-1-4614-6288-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-1-4899-9373-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
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About this book

The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems. Over the last three decades, through the efforts of theoretical physicists and mathematicians, the essential aspects of the Parisi solution were clarified and proved mathematically. The core ideas of the theory that emerged are the subject of this book, including the recent solution of the Parisi ultrametricity conjecture and a conceptually simple proof of the Parisi formula for the free energy. The treatment is self-contained and should be accessible to graduate students with a background in probability theory, with no prior knowledge of spin glasses. The methods involved in the analysis of the Sherrington-Kirkpatrick model also serve as a good illustration of such classical topics in probability as the Gaussian interpolation and concentration of measure, Poisson processes, and representation results for exchangeable arrays.

About the authors

Dmitry Panchenko is Professor of Mathematics at Texas A&M University.

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)

Table of contents (4 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-6289-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-1-4614-6288-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-1-4899-9373-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Sherrington-Kirkpatrick Model
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-6289-7
DOI
10.1007/978-1-4614-6289-7
Hardcover ISBN
978-1-4614-6288-0
Softcover ISBN
978-1-4899-9373-1
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XII, 156
Topics