Statistical Mechanics of Disordered Systems PDF Download
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Author: Anton Bovier
Publisher: Cambridge University Press
ISBN: 0521849918
Category : Mathematics
Languages : en
Pages : 297
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Book Description
Publisher Description
Author: Anton Bovier
Publisher: Cambridge University Press
ISBN: 0521849918
Category : Mathematics
Languages : en
Pages : 297
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Book Description
Publisher Description
Author: Sacha Friedli
Publisher: Cambridge University Press
ISBN: 1107184827
Category : Mathematics
Languages : en
Pages : 643
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Book Description
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Author: Charles M. Newman
Publisher: Springer Science & Business Media
ISBN: 9783764357771
Category : Mathematics
Languages : en
Pages : 100
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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: Andrea Puglisi
Publisher: MDPI
ISBN: 3038970573
Category : Mathematics
Languages : en
Pages : 335
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Book Description
This book is a printed edition of the Special Issue "Thermodynamics and Statistical Mechanics of Small Systems" that was published in Entropy
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: Manuel Osvaldo Cáceres
Publisher: Springer
ISBN: 9783319846811
Category : Science
Languages : en
Pages : 556
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Book Description
This textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are described in sections and specific exercises throughout the text, as well as in appendices. Physical-mathematical motivation is the main driving force for the development of this text. It presents the academic topics of probability theory and stochastic processes as well as new educational aspects in the presentation of non-equilibrium statistical theory and stochastic differential equations.. In particular it discusses the problem of irreversibility in that context and the dynamics of Fokker-Planck. An introduction on fluctuations around metastable and unstable points are given. It also describes relaxation theory of non-stationary Markov periodic in time systems. The theory of finite and infinite transport in disordered networks, with a discussion of the issue of anomalous diffusion is introduced. Further, it provides the basis for establishing the relationship between quantum aspects of the theory of linear response and the calculation of diffusion coefficients in amorphous systems.
Author:
Publisher:
ISBN: 9780511168680
Category : Mathematical statistics
Languages : en
Pages : 312
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Book Description
A self-contained graduate-level introduction to the statistical mechanics of disordered systems. In three parts, the book treats basic statistical mechanics; disordered lattice spin systems; and latest developments in the mathematical understanding of mean-field spin glass models. It assumes basic knowledge of classical physics and working knowledge of graduate-level probability theory.
Author: A. J. Berlinsky
Publisher: Springer Nature
ISBN: 3030281876
Category : Science
Languages : en
Pages : 609
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Book Description
In a comprehensive treatment of Statistical Mechanics from thermodynamics through the renormalization group, this book serves as the core text for a full-year graduate course in statistical mechanics at either the Masters or Ph.D. level. Each chapter contains numerous exercises, and several chapters treat special topics which can be used as the basis for student projects. The concept of scaling is introduced early and used extensively throughout the text. At the heart of the book is an extensive treatment of mean field theory, from the simplest decoupling approach, through the density matrix formalism, to self-consistent classical and quantum field theory as well as exact solutions on the Cayley tree. Proceeding beyond mean field theory, the book discusses exact mappings involving Potts models, percolation, self-avoiding walks and quenched randomness, connecting various athermal and thermal models. Computational methods such as series expansions and Monte Carlo simulations are discussed, along with exact solutions to the 1D quantum and 2D classical Ising models. The renormalization group formalism is developed, starting from real-space RG and proceeding through a detailed treatment of Wilson’s epsilon expansion. Finally the subject of Kosterlitz-Thouless systems is introduced from a historical perspective and then treated by methods due to Anderson, Kosterlitz, Thouless and Young. Altogether, this comprehensive, up-to-date, and engaging text offers an ideal package for advanced undergraduate or graduate courses or for use in self study.
Author: A. Engel
Publisher: Cambridge University Press
ISBN: 9780521774796
Category : Computers
Languages : en
Pages : 346
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Book Description
Learning is one of the things that humans do naturally, and it has always been a challenge for us to understand the process. Nowadays this challenge has another dimension as we try to build machines that are able to learn and to undertake tasks such as datamining, image processing and pattern recognition. We can formulate a simple framework, artificial neural networks, in which learning from examples may be described and understood. The contribution to this subject made over the last decade by researchers applying the techniques of statistical mechanics is the subject of this book. The authors provide a coherent account of various important concepts and techniques that are currently only found scattered in papers, supplement this with background material in mathematics and physics and include many examples and exercises to make a book that can be used with courses, or for self-teaching, or as a handy reference.
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.
