Introduction to the Replica Theory of Disordered Statistical Systems

This book describes the statistical mechanics of classical spin systems with quenched disorder. The first part of the book covers the physics of spin-glass states using results obtained within the framework of the mean field theory of spin glasses. The technique of replica symmetry breaking is explained in detail, along with a discussion of the underlying physics. The second part is devoted to the theory of critical phenomena in the presence of weak quenched disorder. This includes a systematic derivation of the traditional renormalization group theory, which is then used to obtain a new 'random' critical regime in disordered vector ferromagnets and in the two-dimensional Ising model. The third part of the book describes other types of disordered systems, relating to new results at the frontiers of modern research. The book is suitable for graduate students and researchers in the field of statistical mechanics of disordered systems.

'… principal strength is that it provides a clear introduction to the mathematical machinery of RSB, accessible to an advanced graduate student interested in working in the statistical mechanics of disordered systems. For this reason alone it should be part of the library of any theorist working in these areas … Dotsenko's book will remain an important contribution.' Daniel L. Stein, Physics Today, 'The breadth of the exposition, and in particular the fact that also non-mean field systems are covered, is the main merit of this text and illustrates the wide range of applicability of this method … the book will be a useful reference for the researcher and a reasonable first introduction to the field for graduate students entering the field.' A. Bovier, Zentralblatt MATH