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Topics in Disordered Systems (Paperback, 1997 ed.)
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Topics in Disordered Systems (Paperback, 1997 ed.)
Series: Lectures in Mathematics. ETH Zurich
Expected to ship within 10 - 15 working days
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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.)
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