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Statistical Mechanics Of Lattice Systems

Statistical Mechanics of Lattice Systems PDF
Author: David Lavis
Publisher: Springer Science & Business Media
ISBN: 3662100207
Size: 38.67 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 430
View: 1157

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Most of the interesting and difficult problems in statistical mechanics arise when the constituent particles of the system interact with each other with pair or multipartiele energies. The types of behaviour which occur in systems because of these interactions are referred to as cooperative phenomena giving rise in many cases to phase transitions. This book and its companion volume (Lavis and Bell 1999, referred to in the text simply as Volume 1) are princi pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this subject has developed very rapidly over the last thirty years. ' In our choice of topics we have tried to present a good range of fundamental theory and of applications, some of which reflect our own interests. A broad division of material can be made between exact results and ap proximation methods. We have found it appropriate to inelude some of our discussion of exact results in this volume and some in Volume 1. Apart from this much of the discussion in Volume 1 is concerned with mean-field theory. Although this is known not to give reliable results elose to a critical region, it often provides a good qualitative picture for phase diagrams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available. In this volume our main concern is with scaling theory, algebraic methods and the renormalization group.

The Statistical Mechanics Of Quantum Lattice Systems

The Statistical Mechanics of Quantum Lattice Systems PDF
Author:
Publisher: European Mathematical Society
ISBN: 9783037190708
Size: 53.17 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 379
View: 3355

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Quantum statistical mechanics plays a major role in many fields such as thermodynamics, plasma physics, solid-state physics, and the study of stellar structure. While the theory of quantum harmonic oscillators is relatively simple, the case of anharmonic oscillators, a mathematical model of a localized quantum particle, is more complex and challenging. Moreover, infinite systems of interacting quantum anharmonic oscillators possess interesting ordering properties with respect to quantum stabilization. This book presents a rigorous approach to the statistical mechanics of such systems, in particular with respect to their actions on a crystal lattice. The text is addressed to both mathematicians and physicists, especially those who are concerned with the rigorous mathematical background of their results and the kind of problems that arise in quantum statistical mechanics. The reader will find here a concise collection of facts, concepts, and tools relevant for the application of path integrals and other methods based on measure and integration theory to problems of quantum physics, in particular the latest results in the mathematical theory of quantum anharmonic crystals. The methods developed in the book are also applicable to other problems involving infinitely many variables, for example, in biology and economics.

Statistical Mechanics Of Lattice Systems

Statistical Mechanics of Lattice Systems PDF
Author: David Lavis
Publisher: Springer Science & Business Media
ISBN: 9783540644361
Size: 70.59 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 430
View: 2049

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Most of the interesting and difficult problems in statistical mechanics arise when the constituent particles of the system interact with each other with pair or multipartiele energies. The types of behaviour which occur in systems because of these interactions are referred to as cooperative phenomena giving rise in many cases to phase transitions. This book and its companion volume (Lavis and Bell 1999, referred to in the text simply as Volume 1) are princi pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this subject has developed very rapidly over the last thirty years. ' In our choice of topics we have tried to present a good range of fundamental theory and of applications, some of which reflect our own interests. A broad division of material can be made between exact results and ap proximation methods. We have found it appropriate to inelude some of our discussion of exact results in this volume and some in Volume 1. Apart from this much of the discussion in Volume 1 is concerned with mean-field theory. Although this is known not to give reliable results elose to a critical region, it often provides a good qualitative picture for phase diagrams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available. In this volume our main concern is with scaling theory, algebraic methods and the renormalization group.

Operator Algebras And Quantum Statistical Mechanics Ii

Operator Algebras and Quantum Statistical Mechanics II PDF
Author: Ola Bratteli
Publisher: Springer Science & Business Media
ISBN: 3662090899
Size: 68.91 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 507
View: 138

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For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Algebraic Methods In Statistical Mechanics And Quantum Field Theory

Algebraic Methods in Statistical Mechanics and Quantum Field Theory PDF
Author: Dr. Gérard G. Emch
Publisher: Courier Corporation
ISBN: 0486151719
Size: 74.20 MB
Format: PDF
Category : Science
Languages : en
Pages : 352
View: 6630

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This systematic algebraic approach offers a careful formulation of the problems' physical motivations as well as self-contained descriptions of the mathematical methods for arriving at solutions. 1972 edition.

Statistical Mechanics Of Lattice Systems

Statistical Mechanics of Lattice Systems PDF
Author: Sacha Friedli
Publisher: Cambridge University Press
ISBN: 1316884937
Size: 77.45 MB
Format: PDF
Category : Mathematics
Languages : en
Pages :
View: 7504

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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.

The Statistical Mechanics Of Lattice Gases Volume I

The Statistical Mechanics of Lattice Gases  Volume I PDF
Author: Barry Simon
Publisher: Princeton University Press
ISBN: 1400863430
Size: 30.67 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 536
View: 2911

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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.

Operator Algebras And Quantum Statistical Mechanics

Operator Algebras and Quantum Statistical Mechanics PDF
Author: Ola Bratteli
Publisher: Springer Science & Business Media
ISBN: 3662034441
Size: 33.79 MB
Format: PDF
Category : Science
Languages : en
Pages : 517
View: 7617

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For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Noncommutative Structures In Mathematics And Physics

Noncommutative Structures in Mathematics and Physics PDF
Author: S. Duplij
Publisher: Springer Science & Business Media
ISBN: 9401008361
Size: 75.69 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 484
View: 1478

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A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

Analysis And Operator Theory

Analysis and Operator Theory PDF
Author: Themistocles M. Rassias
Publisher: Springer
ISBN: 3030126617
Size: 53.14 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 416
View: 4658

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Dedicated to Tosio Kato’s 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics. Survey papers and in-depth technical papers emphasize linear and nonlinear analysis, operator theory, partial differential equations, and functional analysis including nonlinear evolution equations, the Korteweg–de Vries equation, the Navier–Stokes equation, and perturbation theory of linear operators. The Kato inequality, the Kato type matrix limit theorem, the Howland–Kato commutator problem, the Kato-class of potentials, and the Trotter–Kato product formulae are discussed and analyzed. Graduate students, research mathematicians, and applied scientists will find that this book provides comprehensive insight into the significance of Tosio Kato’s impact to research in analysis and operator theory.

Entropy And The Quantum Ii

Entropy and the Quantum II PDF
Author: Robert Sims
Publisher: American Mathematical Soc.
ISBN: 0821868985
Size: 57.52 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 224
View: 3310

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The goal of the Entropy and the Quantum schools has been to introduce young researchers to some of the exciting current topics in mathematical physics. These topics often involve analytic techniques that can easily be understood with a dose of physical intuition. In March of 2010, four beautiful lectures were delivered on the campus of the University of Arizona. They included Isoperimetric Inequalities for Eigenvalues of the Laplacian by Rafael Benguria, Universality of Wigner Random Matrices by Laszlo Erdos, Kinetic Theory and the Kac Master Equation by Michael Loss, and Localization in Disordered Media by Gunter Stolz. Additionally, there were talks by other senior scientists and a number of interesting presentations by junior participants. The range of the subjects and the enthusiasm of the young speakers are testimony to the great vitality of this field, and the lecture notes in this volume reflect well the diversity of this school.

The Statistical Mechanics Of Financial Markets

The Statistical Mechanics of Financial Markets PDF
Author: Johannes Voit
Publisher: Springer Science & Business Media
ISBN: 3662044234
Size: 79.81 MB
Format: PDF, ePub, Docs
Category : Science
Languages : en
Pages : 220
View: 1101

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A careful examination of the interaction between physics and finance. It takes a look at the 100-year-long history of co-operation between the two fields and goes on to provide new research results on capital markets - taken from the field of statistical physics. The random walk model, well known in physics, is one good example of where the two disciplines meet. In the world of finance it is the basic model upon which the Black-Scholes theory of option pricing and hedging has been built. The underlying assumptions are discussed using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion. On this basis, new theories of derivative pricing and risk control can be formulated.

Equilibrium Statistical Mechanics Of Lattice Models

Equilibrium Statistical Mechanics of Lattice Models PDF
Author: David A. Lavis
Publisher: Springer
ISBN: 9401794308
Size: 73.99 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 793
View: 1549

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Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm—Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg--Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi--Hijmans--De Boer hierarchy of approximations. In Part III the use of algebraic, transformation and decoration methods to obtain exact system information is considered. This is followed by an account of the use of transfer matrices for the location of incipient phase transitions in one-dimensionally infinite models and for exact solutions for two-dimensionally infinite systems. The latter is applied to a general analysis of eight-vertex models yielding as special cases the two-dimensional Ising model and the six-vertex model. The treatment of exact results ends with a discussion of dimer models. In Part IV series methods and real-space renormalization group transformations are discussed. The use of the De Neef—Enting finite-lattice method is described in detail and applied to the derivation of series for a number of model systems, in particular for the Potts model. The use of Pad\'e, differential and algebraic approximants to locate and analyze second- and first-order transitions is described. The realization of the ideas of scaling theory by the renormalization group is presented together with treatments of various approximation schemes including phenomenological renormalization. Part V of the book contains a collection of mathematical appendices intended to minimise the need to refer to other mathematical sources.

Statistical Mechanics

Statistical Mechanics PDF
Author: Giovanni Gallavotti
Publisher: Springer Science & Business Media
ISBN: 3662039524
Size: 27.14 MB
Format: PDF
Category : Science
Languages : en
Pages : 342
View: 2333

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This clear book presents a critical and modern analysis of the conceptual foundations of statistical mechanics as laid down in Boltzmann's works. The author emphasises the relation between microscopic reversibility and macroscopic irreversibility, explaining fundamental concepts in detail.