Download or read book The Statistical Mechanics of Lattice Gases Volume I written by Barry Simon and published by Princeton University Press. This book was released on 2014-07-14 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: A state-of-the-art survey of both classical and quantum lattice gas models, this two-volume work will cover the rigorous mathematical studies of such models as the Ising and Heisenberg, an area in which scientists have made enormous strides during the past twenty-five years. This first volume addresses, among many topics, the mathematical background on convexity and Choquet theory, and presents an exhaustive study of the pressure including the Onsager solution of the two-dimensional Ising model, a study of the general theory of states in classical and quantum spin systems, and a study of high and low temperature expansions. The second volume will deal with the Peierls construction, infrared bounds, Lee-Yang theorems, and correlation inequality. This comprehensive work will be a useful reference not only to scientists working in mathematical statistical mechanics but also to those in related disciplines such as probability theory, chemical physics, and quantum field theory. It can also serve as a textbook for advanced graduate students. Originally published in 1993. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book The Statistical Mechanics of Lattice Gases written by Barry Simon and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Mechanics of Lattice Systems written by Sacha Friedli and published by Cambridge University Press. This book was released on 2017-11-23 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Download or read book Convexity in the Theory of Lattice Gases written by Robert B. Israel and published by Princeton University Press. This book was released on 2015-03-08 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Robert Israel considers classical and quantum lattice systems in terms of equilibrium statistical mechanics. He is especially concerned with the characterization of translation-invariant equilibrium states by a variational principle and the use of convexity in studying these states. Arthur Wightman's Introduction gives a general and historical perspective on convexity in statistical mechanics and thermodynamics. Professor Israel then reviews the general framework of the theory of lattice gases. In addition to presenting new and more direct proofs of some known results, he uses a version of a theorem by Bishop and Phelps to obtain existence results for phase transitions. Furthermore, he shows how the Gibbs Phase Rule and the existence of a wide variety of phase transitions follow from the general framework and the theory of convex functions. While the behavior of some of these phase transitions is very "pathological," others exhibit more "reasonable" behavior. As an example, the author considers the isotropic Heisenberg model. Formulating a version of the Gibbs Phase Rule using Hausdorff dimension, he shows that the finite dimensional subspaces satisfying this phase rule are generic. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Statistical Mechanics of Lattice Systems written by David Lavis and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work provides a comprehensive study of the statistical mechanics of lattice models. It introduces readers to the main topics and the theory of phase transitions, building on a firm mathematical and physical basis. Volume 1 contains an account of mean-field and cluster variation methods successfully used in many applications in solid-state physics and theoretical chemistry, as well as an account of exact results for the Ising and six-vertex models and those derivable by transformation methods.
Download or read book Statistical Mechanics of Lattice Systems written by Sacha Friedli and published by Cambridge University Press. This book was released on 2017-11-23 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This motivating textbook gives a friendly, rigorous introduction to fundamental concepts in equilibrium statistical mechanics, covering a selection of specific models, including the Curie–Weiss and Ising models, the Gaussian free field, O(n) models, and models with Kać interactions. Using classical concepts such as Gibbs measures, pressure, free energy, and entropy, the book exposes the main features of the classical description of large systems in equilibrium, in particular the central problem of phase transitions. It treats such important topics as the Peierls argument, the Dobrushin uniqueness, Mermin–Wagner and Lee–Yang theorems, and develops from scratch such workhorses as correlation inequalities, the cluster expansion, Pirogov–Sinai Theory, and reflection positivity. Written as a self-contained course for advanced undergraduate or beginning graduate students, the detailed explanations, large collection of exercises (with solutions), and appendix of mathematical results and concepts also make it a handy reference for researchers in related areas.
Download or read book Statistical Mechanics of Driven Diffusive Systems written by and published by Elsevier. This book was released on 1995-07-24 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Far-from-equilibrium phenomena, while abundant in nature, are not nearly as well understood as their equilibrium counterparts. On the theoretical side, progress is slowed by the lack of a simple framework, such as the Boltzmann-Gbbs paradigm in the case of equilibrium thermodynamics. On the experimental side, the enormous structural complexity of real systems poses serious obstacles to comprehension.Similar difficulties have been overcome in equilibrium statistical mechanics by focusing on model systems. Even if they seem too simplistic for known physical systems, models give us considerable insight, provided they capture the essential physics. They serve as important theoretical testing grounds where the relationship between the generic physical behavior and the key ingredients of a successful theory can be identified and understood in detail.Within the vast realm of non-equilibrium physics, driven diffusive systems form a subset with particularly interesting properties. As a prototype model for these systems, the driven lattice gas was introduced roughly a decade ago. Since then, a number of surprising phenomena have been discovered including singular correlations at generic temperatures, as well as novel phase transitions, universality classes, and interfacial instabilities. This book summarizes current knowledge on driven systems, from apedagogical discussion of the original driven lattice gas to a brief survey of related models. Given that the topic is far from closed, much emphasis is placed on detailing open questions and unsolved problems as an incentive for the reader to pursue thesubject further.Provides a summary of current knowledge on driven diffusive systemsEmphasis is placed on detailing open questions and unsolved problemsCovers the entire subject from original driven lattice gas to a survey of related models
Download or read book Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems written by Jean-René Chazottes and published by Springer Science & Business Media. This book was released on 2005-07-06 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the dynamics of coupled map lattices (CML) and of related spatially extended systems. It will be useful to post-graduate students and researchers seeking an overview of the state-of-the-art and of open problems in this area of nonlinear dynamics. The special feature of this book is that it describes the (mathematical) theory of CML and some related systems and their phenomenology, with some examples of CML modeling of concrete systems (from physics and biology). More precisely, the book deals with statistical properties of (weakly) coupled chaotic maps, geometric aspects of (chaotic) CML, monotonic spatially extended systems, and dynamical models of specific biological systems.
Download or read book Doing Mathematics Convention Subject Calculation Analogy 2nd Edition written by Martin H Krieger and published by World Scientific. This book was released on 2015-01-15 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doing Mathematics discusses some ways mathematicians and mathematical physicists do their work and the subject matters they uncover and fashion. The conventions they adopt, the subject areas they delimit, what they can prove and calculate about the physical world, and the analogies they discover and employ, all depend on the mathematics — what will work out and what won't. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connections between algebra and topology, and the series of rigorous proofs of the stability of matter. The many and varied solutions to the two-dimensional Ising model of ferromagnetism make sense as a whole when they are seen in an analogy developed by Richard Dedekind in the 1880s to algebraicize Riemann's function theory; by Robert Langlands' program in number theory and representation theory; and, by the analogy between one-dimensional quantum mechanics and two-dimensional classical statistical mechanics. In effect, we begin to see 'an identity in a manifold presentation of profiles,' as the phenomenologists would say.This second edition deepens the particular examples; it describe the practical role of mathematical rigor; it suggests what might be a mathematician's philosophy of mathematics; and, it shows how an 'ugly' first proof or derivation embodies essential features, only to be appreciated after many subsequent proofs. Natural scientists and mathematicians trade physical models and abstract objects, remaking them to suit their needs, discovering new roles for them as in the recent case of the Painlevé transcendents, the Tracy-Widom distribution, and Toeplitz determinants. And mathematics has provided the models and analogies, the ordinary language, for describing the everyday world, the structure of cities, or God's infinitude.
Download or read book Convex Functions and Their Applications written by Constantin P. Niculescu and published by Springer. This book was released on 2018-06-08 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thorough introduction to an important area of mathematics Contains recent results Includes many exercises
Download or read book Lattice Gas Cellular Automata and Lattice Boltzmann Models written by Dieter A. Wolf-Gladrow and published by Springer Science & Business Media. This book was released on 2000-02-18 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.
Download or read book Statistical Mechanics written by R.K. Pathria and published by Elsevier. This book was released on 2017-02-21 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Mechanics discusses the fundamental concepts involved in understanding the physical properties of matter in bulk on the basis of the dynamical behavior of its microscopic constituents. The book emphasizes the equilibrium states of physical systems. The text first details the statistical basis of thermodynamics, and then proceeds to discussing the elements of ensemble theory. The next two chapters cover the canonical and grand canonical ensemble. Chapter 5 deals with the formulation of quantum statistics, while Chapter 6 talks about the theory of simple gases. Chapters 7 and 8 examine the ideal Bose and Fermi systems. In the next three chapters, the book covers the statistical mechanics of interacting systems, which includes the method of cluster expansions, pseudopotentials, and quantized fields. Chapter 12 discusses the theory of phase transitions, while Chapter 13 discusses fluctuations. The book will be of great use to researchers and practitioners from wide array of disciplines, such as physics, chemistry, and engineering.
Download or read book Statistical Mechanics written by Terrell L. Hill and published by Courier Corporation. This book was released on 2013-04-26 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Standard text covers classical statistical mechanics, quantum statistical mechanics, relation of statistical mechanics to thermodynamics, plus fluctuations, theory of imperfect gases and condensation, distribution functions and the liquid state, more.
Download or read book Thermal aspects of field theories written by Adailton Azevêdo Araújo Filho and published by Amazon.com. This book was released on 2022-06-30 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focus on examining the thermodynamic properties of various prominent field theories concerning high-energy and condensed matter physics. We make the usage of the theory of ensembles to perform our analysis. At the beginning, we supply the thermodynamic properties based on the formalism of canonical ensemble to the Aharonov-Bohm quantum ring considering both scenarios: the relativistic and the non-relativistic cases. Next, we construct a model in order to study quantum gases. In this context, we examine bosons, fermions and spinless particles within the grand-canonical ensemble taking into account two different approaches: interacting and noninteracting particles. To corroborate our results, we apply them to the Bose-Einstein condensate and to the helium dimmers. The same approach is applied considering rather Lorentz violation. Moreover, in this context, we also propose two applications to support our theoretical calculations: phosphorene layers and spin precession of quantum gases. Next, the thermodynamic properties are investigated as well to a variety of models/theories (regarding different energy dispersion relations) when the Lorentz symmetry is no longer maintained within the canonical ensemble formalism. To these cases, three distinct thermal scenarios of the universe are considered: the cosmic microwave background, the electroweak epoch, and the inflationary period.
Download or read book Environmental Research Papers written by and published by . This book was released on 1995 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods of Contemporary Mathematical Statistical Physics written by Marek Biskup and published by Springer. This book was released on 2009-07-31 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools. It presents new results on phase transitions for gradient lattice models.
Download or read book Random Walks Critical Phenomena and Triviality in Quantum Field Theory written by Roberto Fernandez and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.
