Scaling And Renormalization In Statistical Physics
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Scaling and Renormalization in Statistical Physics by John Cardy Pdf
This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. It begins with a brief review of phase transitions in simple systems, then goes on to introduce the core ideas of the renormalisation group.
This textbook provides a comprehensive, yet accessible, introduction to statistical mechanics. Crafted and class-tested over many years of teaching, it carefully guides advanced undergraduate and graduate students who are encountering statistical mechanics for the first time through this – sometimes – intimidating subject. The book provides a strong foundation in thermodynamics and the ensemble formalism of statistical mechanics. An introductory chapter on probability theory is included. Applications include degenerate Fermi systems, Bose-Einstein condensation, cavity radiation, phase transitions, and critical phenomena. The book concludes with a treatment of scaling theories and the renormalization group. In addition, it provides clear descriptions of how to understand the foundational mathematics and physics involved and includes exciting case studies of modern applications of the subject in physics and wider interdisciplinary areas. Key Features: Presents the subject in a clear and entertaining style which enables the author to take a sophisticated approach whilst remaining accessible Contains contents that have been carefully reviewed with a substantial panel to ensure that coverage is appropriate for a wide range of courses, worldwide Accompanied by volumes on thermodynamics and non-equilibrium statistical mechanics, which can be used in conjunction with this book, on courses which cover both thermodynamics and statistical mechanics
The material presented in this invaluable textbook has been tested in two courses. One of these is a graduate-level survey of statistical physics; the other, a rather personal perspective on critical behavior. Thus, this book defines a progression starting at the book-learning part of graduate education and ending in the midst of topics at the research level. To supplement the research-level side the book includes some research papers. Several of these are classics in the field, including a suite of six works on self-organized criticality and complexity, a pair on diffusion-limited aggregation, some papers on correlations near critical points, a few of the basic sources on the development of the real-space renormalization group, and several papers on magnetic behavior in a plain geometry. In addition, the author has included a few of his own papers.
Lectures On Phase Transitions And The Renormalization Group by Nigel Goldenfeld Pdf
Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.
Statistical Physics of Particles by Mehran Kardar Pdf
Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.
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.
This text fills a gap between undergraduate and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretation, proceeds to the epsilon-expansion and ends with the first-order corrections to critical exponents beyond mean-field theory.
Equilibrium Statistical Mechanics of Lattice Models by David A. Lavis Pdf
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.
Advanced Statistical Mechanics by Jian-sheng Wang Pdf
This short textbook covers roughly 13 weeks of lectures on advanced statistical mechanics at the graduate level. It starts with an elementary introduction to the theory of ensembles from classical mechanics, and then goes on to quantum statistical mechanics with density matrix. These topics are covered concisely and briefly. The advanced topics cover the mean-field theory for phase transitions, the Ising models and their exact solutions, and critical phenomena and their scaling theory. The mean-field theories are discussed thoroughly with several different perspectives — focusing on a single degree, or using Feynman-Jensen-Bogoliubov inequality, cavity method, or Landau theory. The renormalization group theory is mentioned only briefly. As examples of computational and numerical approach, there is a chapter on Monte Carlo method including the cluster algorithms. The second half of the book studies nonequilibrium statistical mechanics, which includes the Brownian motion, the Langevin and Fokker-Planck equations, Boltzmann equation, linear response theory, and the Jarzynski equality. The book ends with a brief discussion of irreversibility. The topics are supplemented by problem sets (with partial answers) and supplementary readings up to the current research, such as heat transport with a Fokker-Planck approach.
J. J. Binney,N. J. Dowrick,A. J. Fisher,M. E. J. Newman
Author : J. J. Binney,N. J. Dowrick,A. J. Fisher,M. E. J. Newman Publisher : Oxford University Press Page : 477 pages File Size : 52,9 Mb Release : 1992-06-11 Category : Science ISBN : 9780191660566
The Theory of Critical Phenomena by J. J. Binney,N. J. Dowrick,A. J. Fisher,M. E. J. Newman Pdf
The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.
Elements of Phase Transitions and Critical Phenomena by Hidetoshi Nishimori,Gerardo Ortiz Pdf
As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japanese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the text useful for self-teaching, as well as for classroom learning.
