Topics in Disordered Systems (Lectures in Mathematics. ETH Zürich) - Softcover

Newman, Charles M.

Softcover

ISBN 10: 3764357770 ISBN 13: 9783764357771

Publisher: Birkhäuser, 1997

Synopsis

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.)

About this title

Review

"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

Synopsis

Disordered systems are statistical mechanics models in random environments. This text considers the equilibrium properties of a few examples of disordered Ising models from a probability theory and mathematical physics approach, but the material should be of interest 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 nunmber of ground states (at zero temperature) or the nunber of pure Gibbs states (at nonzero temperatures), and these questions are often connected to issues concerning percolation and related models of geometric or combinatorial probability. The conceptual issue of how to approach the thermodynamic (i.e. infinite volume) in systems which may have many complex competing states is considered, along with the more specific problem of whether and in what sense Parisi's analysis of the meanfield (or "infinite-range") model is relevant with regard to the low temperature behaviour of short-range spin glasses.

Edition details

• Publisher: Birkhäuser
• Publication date: 1997
• Language: English
• ISBN 10: 3764357770
• ISBN 13: 9783764357771
• Binding: Paperback
• Number of pages: 96