The Sherrington-Kirkpatrick Model

Beschreibung

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.
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.
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

Autor*in

Dmitry Panchenko

Themen in »The Sherrington-Kirkpatrick Model«

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

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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)

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