Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Mean Field Models for Spin Glasses

Volume II: Advanced Replica-Symmetry and Low Temperature

Authors: Talagrand, Michel

  • Completely rewritten, updated and enlarged edition of Talagrand's Ergebnisse Vol. 46: "Spin Glasses: A Challenge for Mathematicians" (2003) in two volumes
  • Will bring the reader with no previous knowledge of Spin Glasses to the frontier of current research
  • The only fully rigorous treatise of this scale on the subject
  • The present second volume contains a large amount of new results obtained after the publication of the first edition.
see more benefits

Buy this book

eBook $159.00
price for USA (gross)
  • ISBN 978-3-642-22253-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $209.00
price for USA
  • ISBN 978-3-642-22252-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $209.00
price for USA
  • ISBN 978-3-642-27094-9
  • 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
About this book

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.

Reviews

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 contents (9 chapters)

  • The Gardner Formula for the Sphere

    Talagrand, Michel

    Pages 3-47

  • The Gardner Formula for the Discrete Cube

    Talagrand, Michel

    Pages 49-122

  • The Hopfield Model

    Talagrand, Michel

    Pages 123-223

  • The SK Model Without External Field

    Talagrand, Michel

    Pages 225-284

  • The Ghirlanda-Guerra Identities

    Talagrand, Michel

    Pages 287-311

Buy this book

eBook $159.00
price for USA (gross)
  • ISBN 978-3-642-22253-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $209.00
price for USA
  • ISBN 978-3-642-22252-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $209.00
price for USA
  • ISBN 978-3-642-27094-9
  • 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
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Mean Field Models for Spin Glasses
Book Subtitle
Volume II: Advanced Replica-Symmetry and Low Temperature
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
55
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag GmbH Berlin Heidelberg
eBook ISBN
978-3-642-22253-5
DOI
10.1007/978-3-642-22253-5
Hardcover ISBN
978-3-642-22252-8
Softcover ISBN
978-3-642-27094-9
Series ISSN
0071-1136
Edition Number
2
Number of Pages
XII, 632
Additional Information
Originally published as Volume 46 in series "Ergebnisse der Mathematik"
Topics