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 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 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.
Abstract This book provides a thorough introduction to the fascinating world of phase transitions as well as many related topics, including random walks, combinatorial problems, quantum field theory and S-matrix. Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry, and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides an excellent introduction to frontier topics of exactly solved models in statistical mechanics and quantum field theory, renormalization group, conformal models, quantum integrable systems, duality, elastic S-matrix, thermodynamics Bethe ansatz and form factor theory. The clear discussion of physical principles is accompanied by a detailed analysis of several branches of mathematics, distinguished for their elegance and beauty, such as infinite dimensional algebras, conformal mappings, integral equations or modular functions. Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail, paying attention to an overall coherent understanding of physical phenomena. Mathematical background is provided in supplements at the end of each chapter, when appropriate. The chapters are also followed by problems of different levels of difficulty. Advanced undergraduate and graduate students will find a rich and challenging source for improving their skills and for accomplishing a comprehensive learning of the many facets of the subject.
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.
This innovative and modular textbook combines classical topics in thermodynamics, statistical mechanics and many-body theory with the latest developments in condensed matter physics research. Written by internationally renowned experts and logically structured to cater for undergraduate and postgraduate students and researchers, it covers the underlying theoretical principles and includes numerous problems and worked examples to put this knowledge into practice. Three main streams provide a framework for the book; beginning with thermodynamics and classical statistical mechanics, including mean field approximation, fluctuations and the renormalization group approach to critical phenomena. The authors then examine quantum statistical mechanics, covering key topics such as normal Fermi and Luttinger liquids, superfluidity and superconductivity. Finally, they explore classical and quantum kinetics, Anderson localization and quantum interference, and disordered Fermi liquids. Unique in providing a bridge between thermodynamics and advanced topics in condensed matter, this textbook is an invaluable resource to all students of physics.
Abstract Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.
Abstract The methods of coupled quantum field theory, which had great initial success in relativistic elementary particle physics and have subsequently played a major role in the extensive development of non-relativistic quantum many-particle theory and condensed matter physics, are at the core of this book. As an introduction to the subject, this presentation is intended to facilitate delivery of the material in an easily digestible form to students at a relatively early stage of their scientific development, specifically advanced undergraduates (rather than second or third year graduate students), who are mathematically strong physics majors. The mechanism to accomplish this is the early introduction of variational calculus with particle sources and the Schwinger Action Principle, accompanied by Green’s functions, and, in addition, a brief derivation of quantum mechanical ensemble theory introducing statistical thermodynamics. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green’s function equations of motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and non-equilibrium Green’s functions, and their associated spectral representations and approximation procedures. Phenomenology emerging in these discussions includes quantum plasma dynamic, nonlocal screening, plasmons, polaritons, linear electromagnetic response, excitons, polarons, phonons, magnetic Landau quantization, van der Waals interactions, chemisorption, etc. Considerable attention is also given to low-dimensional and nanostructured systems, including quantum wells, wires, dots and superlattices, as well as materials having exceptional conduction properties such as superconductors, superfluids and graphene.