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© 1997

Topics in Disordered Systems

Book

Part of the Lectures in Mathematics ETH Zürich book series (LM)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Charles M. Newman
    Pages 1-3
  3. Charles M. Newman
    Pages 5-15
  4. Charles M. Newman
    Pages 17-26
  5. Charles M. Newman
    Pages 27-46
  6. Charles M. Newman
    Pages 47-64
  7. Back Matter
    Pages 65-88

About this book

Introduction

Disordered systems are statistical mechanics models in random environments. This lecture notes volume concerns the equilibrium properties of a few carefully chosen examples of disordered Ising models. The approach is that of probability theory and mathematical physics, but the subject matter is of interest also to condensed matter physicists, material scientists, applied mathematicians and theoretical computer scientists. (The two main types of systems considered are disordered ferromagnets and spin glasses. The emphasis is on questions concerning the number of ground states (at zero temperature) or the number of pure Gibbs states (at nonzero temperature). A recurring theme is that these questions are connected to interesting issues concerning percolation and related models of geometric/combinatorial probability. One question treated at length concerns the low temperature behavior of short-range spin glasses: whether and in what sense Parisi's analysis of the meanfield (or "infinite-range") model is relevant. Closely related is the more general conceptual issue of how to approach the thermodynamic (i.e., infinite volume) limit in systems which may have many complex competing states. This issue has been addressed in recent joint work by the author and Dan Stein and the book provides a mathematically coherent presentation of their approach.)

Keywords

Gibbs state Helium-Atom-Streuung Rang condensed matter probability theory

Authors and affiliations

  1. 1.Courant Institute of Mathematical SciencesNew YorkUSA

Bibliographic information

  • Book Title Topics in Disordered Systems
  • Authors Charles M. Newman
  • Series Title Lectures in Mathematics ETH Zürich
  • DOI https://doi.org/10.1007/978-3-0348-8912-4
  • Copyright Information Birkhäuser Verlag 1997
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-7643-5777-1
  • eBook ISBN 978-3-0348-8912-4
  • Edition Number 1
  • Number of Pages VIII, 88
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site

Reviews

"The book is accessible to those with an understanding of the basic theory of Gibbs distribution, yet it proceeds almost immediately to the frontiers of research... It is not an attempt to survey the entire field of disordered systems, but it serves as an excellent introduction nonetheless... Newman’s well-written, cohesive presentation should be of great assistance to new and experienced researchers, both mathematicians and physicists."

--Bulletin of the AMS

"A very up-to-date presentation of carefully selected topics... Interesting not only to applied mathematicians and specialists in probability theory, but also to materials scientists and condensed matter physicists."

--Applications of Mathematics