This book presents a systematic and coherent approach to phase transitions and critical phenomena, namely the coherent-anomaly method (CAM theory) based on cluster mean-field approximations. The first part gives a brief review of the CAM theory and the second part a collection of reprints covering the CAM basic calculations, the Blume-Emery-Griffiths model, the extended Baxter model, the quantum Heisenberg model, zero-temperature phase transitions, the KT-transition, spin glasses, the self-avoiding walk, contact processes, branching processes, the gas-liquid transition and even non-equilibrium phase transitions.

This volume is a compilation of papers presented at the International Workshop on the Theory and Applications of the Cluster Variation and Path Probability Methods, held in the city of San Juan, Teotihuacan, Mexico, during June 18-22, 1995. The presentations at the workshop provided a state of the art review of the fundamental aspects of the CVM and PPM and their application to a wide range of problems in statistical mechanics and alloy theory. The volume begins with several articles dealing with the study of the kinetics of ordering in Ising sytems and alloys using the PPM and other classical techniques. These articles are followed by the contribution of Professor Masuo Suzuki on the Coherent Anomaly Method which has added a new dimension to mean field theory, and the CVM in particular, in the study of critical phenomena. The remaining of the volume is dedicated to fundamental aspects and specific applications of the CVM in a wide range of subjects ranging from bulk and surface studies to new areas of inquiry such as the problem of image reconstruction. Since the inception by Prof. Ryoichi Kikuchi of the CVM in 1950 and of the PPM in 1966, the latter after a gestation period of approximately six years, the tech niques have found wide acceptance in the physics and materials science communities. Both methods are properly regarded as seminal contributions to equilibrium and non equilibrium statistical mechanics.

This meeting is devoted to discussing new approaches to critical fluctuation, quantum fluctuation and relaxation phenomena. The main topics include: the study of critical fluctuation, using perturbational expansions, generalized systematic cluster mean-field approximations, the CAM...; possible new systematic approaches to quantum fluctuation including quantum Monte Carlo simulations; and coherent approaches to fluctuation and relaxation in complex systems such as spin glasses.

Contents:Trace Formulae for Levy-Gaussian Measures and Their Application (L Accardi & O G Smolyanov)Mathematical Theory of Early Vision: Historical Note (J J Atick)Unidirectional versus Bi-directional Theory for Trajectory Planning and Control (M Kawato)Relaxations in the Electronic Excited States of Complex Systems (T Kushida)Coherent Approach to Fluctuations (M Suzuki)Simulational and Analytic Studies of Anomalous Relaxation in Disordered Systems (F Yonezawa et al)Work with Pavel Bleher on Eigenvalue Statistics in Integrable Dynamical Systems (F Dyson)and other papers Readership: Applied mathematicians.keywords:

The present volume contains the text of the invited talks delivered at the Eighth International Conference on Recent Progress in Many-Body Theories held at SchloB Seggau, Province of Styria, Austria, during the period August 22-26, 1994. The pro ceedings of the Fifth Conference (Oulu, Finland 1987), the Sixth Conference (Arad, Israel 1989) and the Seventh Conference (Minneapolis, USA 1991) have been published. by Plenum as the first three volumes of this series. Papers from the First Conference (Trieste, Italy 1978) comprise Nuclear Physics volume A328, Nos. 1 and 2, the Second Conference (Oaxtepec, Mexico 1979) was published by Springer-Verlag as volume 142 of "Lecture Notes in Physics," entitled "Recent Progress in Many Body Theories." Vol ume 198 of the same series contains the papers from the Third Conference (Altenberg, 1983). These volumes intend to cover a broad spectrum of current research topics in physics that benefit from the application of many-body theories for their elucidation. At the same time there is a focus on the development and refinement of many-body methods. One of the major aims of the conference series has been to foster the exchange of ideas among physicists working in such diverse areas as nuclear physics, quantum chemistry, complex systems, lattice Hamiltonians, quantum fluids and condensed matter physics. The present volume contains contributions from all these areas. th The conference was dedicated on the occasion of Ludwig Boltzmann's 150 birthday.

The latest volume in the world renowned Solid State Physics series marks the fruition of Founding Editor David Turnbull's outstanding tenure as series editor. Volume 47 presents five articles written by leadingexperts on areas including crystal-melt interfacial tension, order-disorder transformation in alloys, brittle matrix composites, surfaces and interfaces, and magnetoresistance.

Many novel cooperative phenomena found in a variety of systems studied by scientists can be treated using the uniting principles of synergetics. Examples are frustrated and random systems, polymers, spin glasses, neural networks, chemical and biological systems, and fluids. In this book attention is focused on two main problems. First, how local, topological constraints (frustrations) can cause macroscopic cooperative behavior: related ideas initially developed for spin glasses are shown to play key roles also for optimization and the modeling of neural networks. Second, the dynamical constraints that arise from the nonlinear dynamics of the systems: the discussion covers turbulence in fluids, pattern formation, and conventional 1/f noise. The volume will be of interest to anyone wishing to understand the current development of work on complex systems, which is presently one of the most challenging subjects in statistical and condensed matter physics.