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Author: Ilʹi͡a Mikhaĭlovich Lifshit͡s
Publisher: Wiley-VCH
ISBN:
Category : Science
Languages : en
Pages : 488
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Book Description
Focuses on an important aspect of this highly diversified area of condensed state physics: the one-body approximation in the theory of disordered systems. It describes the scope of problems within the framework of this approximation, its use in formulating several basic concepts, and its value in revealing many characteristic features of disordered systems. The book's main focus is on the density of states and the space-time correlation functions, and on their basic thermodynamic and kinetic characteristics. Among the many areas explored are the general properties of the one-body models frequently used and descriptions of selected one-dimensional problems, including closed dynamical equations; these are then used to thoroughly explore the density of states for several systems. In addition, some of the more complex characteristics of one-dimensional disordered systems are examined using the Fokkerr-Planck equations developed earlier in the text. Also includes a description of the general structure of concentration expansions, giving examples of simple applications.
Author: Ilʹi͡a Mikhaĭlovich Lifshit͡s
Publisher: Wiley-VCH
ISBN:
Category : Science
Languages : en
Pages : 488
Get Book
Book Description
Focuses on an important aspect of this highly diversified area of condensed state physics: the one-body approximation in the theory of disordered systems. It describes the scope of problems within the framework of this approximation, its use in formulating several basic concepts, and its value in revealing many characteristic features of disordered systems. The book's main focus is on the density of states and the space-time correlation functions, and on their basic thermodynamic and kinetic characteristics. Among the many areas explored are the general properties of the one-body models frequently used and descriptions of selected one-dimensional problems, including closed dynamical equations; these are then used to thoroughly explore the density of states for several systems. In addition, some of the more complex characteristics of one-dimensional disordered systems are examined using the Fokkerr-Planck equations developed earlier in the text. Also includes a description of the general structure of concentration expansions, giving examples of simple applications.
Author: Viktor Dotsenko
Publisher: Cambridge University Press
ISBN: 9780521021258
Category : Science
Languages : en
Pages : 236
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Book Description
This text describes the statistical mechanics of classical spin systems with quenched disorder. The first part covers the physics of spin-glass states using results obtained within the framework of the mean field theory of spin glasses. 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. In the third part Dotsenko describes other types of disordered systems, relating them 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.
Author: Viktor Dotsenko
Publisher: Cambridge University Press
ISBN: 0521773407
Category : Science
Languages : en
Pages : 236
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Book Description
An introductory book on the statistical mechanics of disordered systems, ideal for graduates and researchers.
Author: Charles M. Newman
Publisher: Birkhäuser
ISBN: 3034889127
Category : Mathematics
Languages : en
Pages : 93
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Book Description
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.)
Author: Anton Bovier
Publisher: Cambridge University Press
ISBN: 0521849918
Category : Mathematics
Languages : en
Pages : 297
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Book Description
Publisher Description
Author: J. M. Ziman
Publisher: Cambridge University Press
ISBN: 9780521292801
Category : Science
Languages : en
Pages : 548
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Book Description
Originally published in 1979, this book discusses how the physical and chemical properties of disordered systems such as liquids, glasses, alloys, amorphous semiconductors, polymer solutions and magnetic materials can be explained by theories based on a variety of mathematical models, including random assemblies of hard spheres, tetrahedrally-bonded networks and lattices of 'spins'. The text describes these models and the various mathematical theories by which the observable properties are derived. Techniques and concepts such as the mean field and coherent approximations, graphical summation, percolation, scaling and the renormalisation group are explained and applied. This book will be of value to anyone with an interest in theoretical and experimental physics.
Author: Dietrich Stauffer
Publisher: CRC Press
ISBN: 1482272377
Category : Science
Languages : en
Pages : 192
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Book Description
This work dealing with percolation theory clustering, criticallity, diffusion, fractals and phase transitions takes a broad approach to the subject, covering basic theory and also specialized fields like disordered systems and renormalization groups.
Author: Paolo M. Ossi
Publisher: Springer Nature
ISBN: 3662684284
Category :
Languages : en
Pages : 380
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Book Description
Author: Armin Bunde
Publisher: Springer Science & Business Media
ISBN: 3642514359
Category : Science
Languages : en
Pages : 363
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Book Description
Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses, and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In 10 chapters written by leading experts in the field, including E. Stanley and B. Mandelbrot, the reader is introduced to basic concepts and techniques in disordered systems and is lead to the forefront of current research. In each chapter the connection between theory and experiment is emphasized, and a special chapter entitled "Fractals and Experiments" presents experimental studies of fractal systems in the laboratory. The book is written pedagogically. It can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field.
Author: Piers Coleman
Publisher: Cambridge University Press
ISBN: 1316432025
Category : Science
Languages : en
Pages : 815
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Book Description
A modern, graduate-level introduction to many-body physics in condensed matter, this textbook explains the tools and concepts needed for a research-level understanding of the correlated behavior of quantum fluids. Starting with an operator-based introduction to the quantum field theory of many-body physics, this textbook presents the Feynman diagram approach, Green's functions and finite-temperature many-body physics before developing the path integral approach to interacting systems. Special chapters are devoted to the concepts of Fermi liquid theory, broken symmetry, conduction in disordered systems, superconductivity and the physics of local-moment metals. A strong emphasis on concepts and numerous exercises make this an invaluable course book for graduate students in condensed matter physics. It will also interest students in nuclear, atomic and particle physics.
