The Sherrington-Kirkpatrick Model | Buch

Cover: 9781461462880 | The Sherrington-Kirkpatrick Model | Dmitry Panchenko | Buch | xii

Rückseite: 9781461462880 | The Sherrington-Kirkpatrick Model | Dmitry Panchenko | Buch | xii

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Sprache: Englisch

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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.

Über den Autor

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

Zusammenfassung

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

Inhaltsverzeichnis

Preface.- 1 The Free Energy and Gibbs Measure.- 2 The Ruelle Probability Cascades.- 3 The Parisi Formula.- 4 Toward a Generalized Parisi Ansatz.- A Appendix.- Bibliography.- Notes and Comments.- References.- Index.

Details

Erscheinungsjahr:	2013
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xii 156 S.
ISBN-13:	9781461462880
ISBN-10:	1461462886
Sprache:	Englisch
Einband:	Gebunden
Autor:	Panchenko, Dmitry
Hersteller:	Springer New York Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 14 mm
Von/Mit:	Dmitry Panchenko
Erscheinungsdatum:	21.02.2013
Gewicht:	0,424 kg

Artikel-ID: 106174055