Lectures on phase transitions and the renormalization group / Nigel Goldenfeld
- Goldenfeld, Nigel
- Boca Raton : CRC Press, 2018.
- Physical Description:
- 1 online resource
- Frontiers in physics ; v. 85
- Cover; Half Title; Title Page; Copyright Page; Dedication; Editor's Foreword; Table of Contents; Preface; Chapter 1: Introduction; 1.1 Scaling and Dimensional Analysis; 1.2 Power Laws in Statistical Physics; 1.2.1 Liquid Gas Critical Point; 1.2.2 Magnetic Critical Point; 1.2.3 Superfluid Transition in 4He; 1.2.4 Self-Avoiding Walk; 1.2.5 Dynamic Critical Phenomena; 1.3 Some Important Questions; 1.4 Historical Development; Exercises; Chapter 2: How Phase Transitions Occur in Principle; 2.1 Review of Statistical Mechanics; 2.2 The Thermodynamic Limit, 2.2.1 Thermodynamic Limit in a Charged System2.2.2 Thermodynamic Limit for Power Law Interactions; 2.3 Phase Boundaries and Phase Transition; 2.3.1 Ambiguity in the Definition of Phase Boundary; 2.3.2 Types of Phase Transition; 2.3.3 Finite Size Effects and the Correlation Length; 2.4 The Role of Models; 2.5 The Ising Model; 2.6 Analytic Properties of the Ising Model; 2.6.1 Convex Functions; 2.6.2 Convexity and the Free Energy Density; 2.7 Symmetry Properties of the Ising Model; 2.7.1 Time Reversal Symmetry; 2.7.2 Sub-Lattice Symmetry; 2.8 Existence of Phase Transitions, 2.8.1 Zero Temperature Phase Diagram2.8.2 Phase Diagram at Non-Zero Temperature: d = 1; 2.8.3 Phase Diagram at Non-Zero Temperature: d = 2; 2.8.4 Impossibility of Phase Transitions; 2.9 Spontaneous Symmetry Breaking; 2.9.1 Probability Distribution; 2.9.2 Continuous Symmetry; 2.10 Ergodicity Breaking; 2.10.1 Illustrative Example; 2.10.2 Symmetry and Its Implications for Ergodicity Breaking; 2.10.3 Example of Replica Symmetry Breaking: Rubber; 2.10.4 Order Parameters and Overlaps in a Classical Spin Glass; 2.10.5 Replica Formalism for Constrained Systems; 2.11 Fluids; 2.12 Lattice Gases, 2.12.1 Lattice Gas Thermodynamics from the Ising Model2.12.2 Derivation of Lattice Gas Model from the Configurational Sum; 2.13 Equivalence in Statistical Mechanics; 2.14 Miscellaneous Remarks; 2.14.1 History of the Thermodynamic Limit; 2.14.2 Do Quantum Effects Matter?; Exercises; Chapter 3: How Phase Transitions Occur in Practice; 3.1 Ad Hoc Solution Methods; 3.1.1 Free Boundary Conditions and H = 0; 3.1.2 Periodic Boundary Conditions and H = 0; 3.1.3 Recursion Method for H = 0; 3.1.4 Effect of Boundary Conditions; 3.2 The Transfer Matrix; 3.3 Phase Transitions; 3.4 Thermodynamic Properties, and 3.5 Spatial Correlations3.5.1 Zero Field: Ad Hoc Method; 3.5.2 Existence of Long Range Order; 3.5.3 Transfer Matrix Method; 3.6 Low Temperature Expansion; 3.6.1 d> 1; 3.6.2 d = 1; 3.7 Mean Field Theory; 3.7.1 Weissâ#x80;#x99; Mean Field Theory; 3.7.2 Spatial Correlations; 3.7.3 How Good Is Mean Field Theory?; Exercises; Chapter 4: Critical Phenomena in Fluids; 4.1 Thermodynamics; 4.1.1 Thermodynamic Potentials; 4.1.2 Phase Diagram; 4.1.3 Landauâ#x80;#x99;s Symmetry Principle; 4.2 Two-Phase Coexistence; 4.2.1 Fluid at Constant Pressure; 4.2.2 Fluid at Constant Temperature; 4.2.3 Maxwellâ#x80;#x99;s Equal Area Rule
- 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.
- 9780429493492 (electronic bk.), 0429493495 (electronic bk.), and 9780429962042
- Bibliography Note:
- Includes bibliographical references and index.
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