This comprehensive work provides a rigorous introduction to statistical mechanics, which aims to relate microscopic properties of matter to observed macroscopic, or bulk, behavior of physical systems. The foundations of statistical mechanics, laid down by Gibbs, are presented in detail along with an introductory chapter on thermodynamics. Other topics covered include model systems and the thermodynamic limit; theories of phase transitions; fluctuations and correlations; exactly solved models; scaling theory; and the renormalization group. An important feature of the book is many problems and worked solutions which provide a timely demonstration of current research activity in the field.
Key features include an elementary introduction to probability, distribution functions, and uncertainty; a review of the concept and significance of energy; and various models of physical systems. 1968 edition.
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.
This book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round.
This modern textbook provides a complete survey of the broad field of statistical mechanics. Based on a series of lectures, it adopts a special pedagogical approach. The authors, both excellent lecturers, clearly distinguish between general principles and their applications in solving problems. Analogies between phase transitions in fluids and magnets using continuum and spin models are emphasized, leading to a better understanding. Such special features as historical notes, summaries, problems, mathematical appendix, computer programs and order of magnitude estimations distinguish this volume from competing works. Due to its ambitious level and an extensive list of references for technical details on advanced topics, this is equally a must for researchers in condensed matter physics, materials science, polymer science, solid state physics, and astrophysics. From the contents Thermostatics: phase stability, phase equilibria, phase transitions; Statistical Mechanics: calculation, correlation functions, ideal classical gases, ideal quantum gases; Interacting Systems: models, computer simulation, mean-field approximation; Interacting Systems beyond Mean-field Theory: scaling and renormalization group, foundations of statistical mechanics "The present book, however, is unique that it both is written in a very pedagogic, easily comprehensible style, and, nevertheless, goes from the basic principles all the way to these modern topics, containing several chapters on the various approaches of mean field theory, and a chapter on computer simulation. A characteristic feature of this book is that often first some qualitative arguments are given, or a "pedestrians's approach", and then a more general and/or more rigorous derivation is presented as well. Particularly useful are also "supplementary notes", pointing out interesting applications and further developments of the subject, a detailed bibliography, problems and historical notes, and many pedagogic figures."
This is a textbook which gradually introduces the student to the statistical mechanical study of the different phases of matter and to the phase transitions between them. Throughout, only simple models of both ordinary and soft matter are used but these are studied in full detail. The subject is developed in a pedagogical manner, starting from the basics, going from the simple ideal systems to the interacting systems, and ending with the more modern topics. The textbook provides the student with a complete overview, intentionally at an introductory level, of the theory of phase transitions. All equations and deductions are included.
Groundbreaking monograph by Nobel Prize winner for researchers and graduate students covers Liouville equation, anharmonic solids, Brownian motion, weakly coupled gases, scattering theory and short-range forces, general kinetic equations, more. 1962 edition.
Isolated systems and thermal equilibrium -- Various reservoirs -- Probability and the general formalism -- Classical statistical mechanics -- Ideal systems -- Interacting particles -- Diagrammatic and functional expansions -- Pair functions -- Functional and perturbation theory -- Inhomogeneous systems -- Coulomb systems -- Computer simulations.
