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" Statistical mechanics : "
A.J. Berlinsky, A.B. Harris.
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BL
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862824
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| Main Entry
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Berlinsky, A. J.
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| Title & Author
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Statistical mechanics : : an introductory graduate course /\ A.J. Berlinsky, A.B. Harris.
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| Publication Statement
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Cham, Switzerland :: Springer,, 2019.
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| Series Statement
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Graduate texts in physics,
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| Page. NO
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1 online resource (xxi, 602 pages) :: illustrations (some color)
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| ISBN
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3030281868
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: 3030281876
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: 3030281884
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: 3030281892
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: 9783030281861
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: 9783030281878
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: 9783030281885
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: 9783030281892
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9783030281861
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Preface; Contents; About the Authors; Part I Preliminaries; 1 Introduction; 1.1 The Role of Statistical Mechanics; 1.2 Examples of Interacting Many-Body Systems; 1.2.1 Solid-Liquid-Gas; 1.2.2 Electron Liquid; 1.2.3 Classical Spins; 1.2.4 Superfluids; 1.2.5 Superconductors; 1.2.6 Quantum Spins; 1.2.7 Liquid Crystals, Polymers, Copolymers; 1.2.8 Quenched Randomness; 1.2.9 Cosmology and Astrophysics; 1.3 Challenges; 1.4 Some Key References; 2 Phase Diagrams; 2.1 Examples of Phase Diagrams; 2.1.1 Solid-Liquid-Gas; 2.1.2 Ferromagnets; 2.1.3 Antiferromagnets; 2.1.4 3He-4He Mixtures
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2.1.5 Pure 3He2.1.6 Percolation; 2.2 Conclusions; 2.3 Exercises; References; 3 Thermodynamic Properties and Relations; 3.1 Preamble; 3.2 Laws of Thermodynamics; 3.3 Thermodynamic Variables; 3.4 Thermodynamic Potential Functions; 3.5 Thermodynamic Relations; 3.5.1 Response Functions; 3.5.2 Mathematical Relations; 3.5.3 Applications; 3.5.4 Consequences of the Third Law; 3.6 Thermodynamic Stability; 3.6.1 Internal Energy as a Thermodynamic Potential; 3.6.2 Stability of a Homogeneous System; 3.6.3 Extremal Properties of the Free Energy; 3.7 Legendre Transformations
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3.8 N as a Thermodynamic Variable3.8.1 Two-Phase Coexistence and P/T Along the Melting Curve; 3.8.2 Physical Interpretation of the Chemical Potential; 3.8.3 General Structure of Phase Transitions; 3.9 Multicomponent Systems; 3.9.1 Gibbs-Duhem Relation; 3.9.2 Gibbs Phase Rule; 3.10 Exercises; References; Part II Basic Formalism; 4 Basic Principles; 4.1 Introduction; 4.2 Density Matrix for a System with Fixed Energy; 4.2.1 Macroscopic Argument; 4.2.2 Microscopic Argument; 4.2.3 Density of States of a Monatomic Ideal Gas; 4.3 System in Contact with an Energy Reservoir
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4.3.1 Two Subsystems in Thermal Contact4.3.2 System in Contact with a Thermal Reservoir; 4.4 Thermodynamic Functions for the Canonical Distribution; 4.4.1 The Entropy; 4.4.2 The Internal Energy and the Helmholtz Free Energy; 4.5 Classical Systems; 4.5.1 Classical Density Matrix; 4.5.2 Gibbs Entropy Paradox; 4.5.3 Irrelevance of Classical Kinetic Energy; 4.6 Summary; 4.7 Exercises; 4.8 Appendix Indistinguishability; References; 5 Examples; 5.1 Noninteracting Subsystems; 5.2 Equipartition Theorem; 5.3 Two-Level System; 5.4 Specific Heat-Finite-Level Scheme; 5.5 Harmonic Oscillator
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5.5.1 The Classical Oscillator5.5.2 The Quantum Oscillator; 5.5.3 Asymptotic Limits; 5.6 Free Rotator; 5.6.1 Classical Rotator; 5.6.2 Quantum Rotator; 5.7 Grüneisen Law; 5.8 Summary; 5.9 Exercises; 6 Basic Principles (Continued); 6.1 Grand Canonical Partition Function; 6.2 The Fixed Pressure Partition Function; 6.3 Grand and Fixed Pressure Partition Functions for a Classical Ideal Gas; 6.3.1 Grand Partition Function of a Classical Ideal Gas; 6.3.2 Constant Pressure Partition Function of a Classical Ideal Gas; 6.4 Overview of Various Partition Functions; 6.5 Product Rule
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| Abstract
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In a comprehensive treatment of Statistical Mechanics from thermodynamics through the renormalization group, this book serves as the core text for a full-year graduate course in statistical mechanics at either the Masters or Ph. D. level. Each chapter contains numerous exercises, and several chapters treat special topics which can be used as the basis for student projects. The concept of scaling is introduced early and used extensively throughout the text. At the heart of the book is an extensive treatment of mean field theory, from the simplest decoupling approach, through the density matrix formalism, to self-consistent classical and quantum field theory as well as exact solutions on the Cayley tree. Proceeding beyond mean field theory, the book discusses exact mappings involving Potts models, percolation, self-avoiding walks and quenched randomness, connecting various athermal and thermal models. Computational methods such as series expansions and Monte Carlo simulations are discussed, along with exact solutions to the 1D quantum and 2D classical Ising models. The renormalization group formalism is developed, starting from real-space RG and proceeding through a detailed treatment of Wilson's epsilon expansion. Finally the subject of Kosterlitz-Thouless systems is introduced from a historical perspective and then treated by methods due to Anderson, Kosterlitz, Thouless and Young. Altogether, this comprehensive, up-to-date, and engaging text offers an ideal package for advanced undergraduate or graduate courses or for use in self study.
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| Subject
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Statistical mechanics.
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| Subject
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Statistical mechanics.
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| Dewey Classification
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530.13
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| LC Classification
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QC174.8
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| Added Entry
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Harris, A. B.
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