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Mean Field Models for Spin Glasses: Volume II: Advanced Replica-Symmetry and Low

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ISBN-13
9783642270949
Book Title
Mean Field Models for Spin Glasses
ISBN
9783642270949
Publication Name
Mean Field Models for Spin Glasses : Volume II: Advanced Replica-Symmetry and Low Temperature
Item Length
9.3in
Publisher
Springer Berlin / Heidelberg
Series
Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge / a Series of Modern Surveys in Mathematics Ser.
Publication Year
2013
Type
Textbook
Format
Trade Paperback
Language
English
Item Height
0.5in
Author
Michel Talagrand
Item Width
6.1in
Item Weight
34.3 Oz
Number of Pages
Xii, 632 Pages

關於產品

Product Information

This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians" in two volumes (this is the 2nd volume). In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The present Volume II contains a considerable amount of new material, in particular all the fundamental low-temperature results obtained after the publication of the first edition.

Product Identifiers

Publisher
Springer Berlin / Heidelberg
ISBN-10
3642270948
ISBN-13
9783642270949
eBay Product ID (ePID)
171892167

Product Key Features

Author
Michel Talagrand
Publication Name
Mean Field Models for Spin Glasses : Volume II: Advanced Replica-Symmetry and Low Temperature
Format
Trade Paperback
Language
English
Series
Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge / a Series of Modern Surveys in Mathematics Ser.
Publication Year
2013
Type
Textbook
Number of Pages
Xii, 632 Pages

Dimensions

Item Length
9.3in
Item Height
0.5in
Item Width
6.1in
Item Weight
34.3 Oz

Additional Product Features

Series Volume Number
55
Number of Volumes
1 Vol.
Lc Classification Number
Qa273.A1-274.9
Edition Number
2
Reviews
From the reviews of the second edition: "This is the second volume of the treatise 'Mean fields models for spin glasses' and it is truly the continuation of the preceding one. ... the book is a book of mathematics expanded around Hamiltonian. The main considered topics are the Gardner formula, the Hopfield model, the SK model, the Parisi formula and the p-spin interaction model. ... This is truly a nice book of condensed mathematics." (Guy Jumarie, Zentralblatt MATH, Vol. 1232, 2012), From the reviews of the second edition: "This is the second volume of the author's treatise Mean field models for spin glasses ... . With its depth and profusion of important techniques, this book ... opens new perspectives in probability theory and statistical mechanics of disordered systems. It will be a source of inspiration for generations of mathematicians." (Francis Comets, Mathematical Reviews, November, 2013) "This is the second volume of the treatise 'Mean fields models for spin glasses' and it is truly the continuation of the preceding one. ... the book is a book of mathematics expanded around Hamiltonian. The main considered topics are the Gardner formula, the Hopfield model, the SK model, the Parisi formula and the p-spin interaction model. ... This is truly a nice book of condensed mathematics." (Guy Jumarie, Zentralblatt MATH, Vol. 1232, 2012)
Table of Content
Part I. Advanced Replica-Symmetry. - The Gardener Formula for the sphere. - The Gardener Formula for the Discrete Cube. - The Hopfield Model. - The SK Model Without External Field. - Part II. Low Temperature. - The Ghirlanda-Guerra Identities. - The High-Temperature Region of the SK Model. - The Parisi Formula. - The Parisi Solution. - The p -spin Interaction Model. - Appendix: Elements of Probability Theory. - References. - Index.
Copyright Date
2011
Topic
Physics / Condensed Matter, Mechanics / General, Probability & Statistics / General, Physics / Mathematical & Computational, Physics / General
Dewey Decimal
530.412
Intended Audience
Scholarly & Professional
Dewey Edition
23
Illustrated
Yes
Genre
Science, Mathematics

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