Statistical Mechanics of Disordered Systems: A Mathematical Perspective
Anton Bovier
Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, recent progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail.
Thể loại:
Năm:
2006
In lần thứ:
1
Nhà xuát bản:
Cambridge University Press
Ngôn ngữ:
english
Trang:
328
ISBN 10:
0521849918
ISBN 13:
9780521849913
Loạt:
Cambridge Series in Statistical and Probabilistic Mathematics
File:
PDF, 4.23 MB
IPFS:
,
english, 2006