Save 40% on select Business & Management books + FREE shipping or 50% on Physics eBooks!

Grundlehren der mathematischen Wissenschaften

The Random-Cluster Model

Authors: Grimmett, Geoffrey R.

Free Preview

Buy this book

eBook 74,96 €
price for Spain (gross)
  • ISBN 978-3-540-32891-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-540-32890-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 93,59 €
price for Spain (gross)
  • ISBN 978-3-642-06943-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

The random-cluster model has emerged in recent years as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. This systematic study includes accounts of the subcritical and supercritical phases, together with clear statements of important open problems. There is an extensive treatment of the first-order (discontinuous) phase transition, as well as a chapter devoted to applications of the random-cluster method to other models of statistical physics.

About the authors

PhD (Oxford 1974) under supervision of John Hammersley and Dominic Welsh. Member of the Mathematics Department of Bristol University (1976-1992), and subsequently appointed to the Professorship of Mathematics Statistics at Cambridge University. Author of around 100 articles and five books in probability and related fields, including Percolation (Springer 1999), Probability and Random Processes (with David Stirzaker, Oxford University Press 2001). Managing Editor of "Probability Theory and Related Fields", 2001-2005.

Reviews

From the reviews:

"This book constitutes an authoritative treatise of the random cluster model and its applications. It will be indispensable for anyone working on this and related subjects and can provide the basis for a graduate course or seminar." (Anton Bovier, Zentralblatt MATH, Vol. 1122 (24), 2007)

"This text is the first reference book devoted to the random-cluster model. The author knows the matter very well, since he is one of the first mathematicians who worked on this model. … This is a very useful book, because it is very well written and collects results that are currently disseminated in the literature." (Olivier Garet, Mathematical Reviews, Issue 2007 m)

"The random-cluster model was discovered in the late 1960s by P. W. Kasteleyn and his doctoral student C. M. Fortuin … . can be used in two ways: as an easily accessible introduction to the field for the newcomer, and as a valuable reference work of the present state of the art for the expert. The book is a must for anyone interested in percolation and mathematical Statistical Mechanics, and will certainly continue the success … ." (Hans-Otto Georgii, Combinatorics, Probability and Computing, Vol. 17, 2008)

"Readership: Probabilists, ranging from graduate students in general to experts on the random-cluster and related models. … The random-cluster model is a generalization of standard bond percolation. … In the random-cluster model, the probability distribution is perturbed by a factor q raised to the number of connected components. … The clarity of the exposition makes the book ideal for graduate students and other novices to the model." (Olle Häggström, International Statistical Review, Vol. 75 (2), 2007)


Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook 74,96 €
price for Spain (gross)
  • ISBN 978-3-540-32891-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-540-32890-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 93,59 €
price for Spain (gross)
  • ISBN 978-3-642-06943-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
The Random-Cluster Model
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
333
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-32891-9
DOI
10.1007/978-3-540-32891-9
Hardcover ISBN
978-3-540-32890-2
Softcover ISBN
978-3-642-06943-7
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XIII, 378
Topics