Theory of Phase Transitions (eBook)
162 Seiten
Elsevier Science (Verlag)
978-1-4831-5849-5 (ISBN)
The book consists of four chapters, wherein the first chapter discusses the Hamiltonian, its symmetry group, and the limit Gibbs distributions corresponding to a given Hamiltonian. The second chapter studies the phase diagrams of lattice models that are considered at low temperatures. The notions of a ground state of a Hamiltonian and the stability of the set of the ground states of a Hamiltonian are also introduced. Chapter 3 presents the basic theorems about lattice models with continuous symmetry, and Chapter 4 focuses on the second-order phase transitions and on the theory of scaling probability distributions, connected to these phase transitions.
Specialists in statistical physics and other related fields will greatly benefit from this publication.
Theory of Phase Transitions: Rigorous Results is inspired by lectures on mathematical problems of statistical physics presented in the Mathematical Institute of the Hungarian Academy of Sciences, Budapest. The aim of the book is to expound a series of rigorous results about the theory of phase transitions. The book consists of four chapters, wherein the first chapter discusses the Hamiltonian, its symmetry group, and the limit Gibbs distributions corresponding to a given Hamiltonian. The second chapter studies the phase diagrams of lattice models that are considered at low temperatures. The notions of a ground state of a Hamiltonian and the stability of the set of the ground states of a Hamiltonian are also introduced. Chapter 3 presents the basic theorems about lattice models with continuous symmetry, and Chapter 4 focuses on the second-order phase transitions and on the theory of scaling probability distributions, connected to these phase transitions. Specialists in statistical physics and other related fields will greatly benefit from this publication.
Front Cover 1
Theory of Phase Transitions: Rigorous Results 4
Copyright Page 5
Table of Contents 6
Preface 8
Chapter 1. Limit Gibbs distributions 10
1. Hamiltonians 10
2. Examples of Hamiltonians 14
3. The definition of limit Gibbs distributions 16
4. Examples 19
5. Existence of limit Gibbs distributions 25
6. Limit Gibbs distributions for continuous fields and for point fields 34
Historical notes and references to Chapter I 36
Chapter 2. Phase diagrams for classical lattice systems. Peierls's method of contours 38
1. Introduction 38
2. Ground states 44
3. Ground states of the perturbed Hamiltonian 46
4. Phase transitions in the two-dimensional Ising ferromagnet 48
5. The Main Theorem and its consequences 52
6. Contours 55
7. Contour models 57
8. Correlation functions of infinite contour models 61
9. Surface tension in contour models 66
10. Proof of the Main Theorem 71
11. Some further remarks 77
Historical notes and references to Chapter II 81
Chapter 3. Lattice systems with continuous symmetry 84
1. Introduction 84
2. Absence of breakdown of continuous symmetry in two-dimensional models 86
3. The Fröhlich–Simon–Spencer theorem on the existence of spontaneous magnetization in the -dimensional classical Heisenberg model, d=3 93
Historical notes and references to Chapter III 103
Chapter 4. Phase transitions of the second kind and the renormalization group method 104
1. Introduction 104
2. Dyson's hierarchical models 106
3. Gaussian solutions 111
4. The domain c < v2
5. Scaling probability distributions 128
6. Gaussian scaling distributions 130
7. The space of Hamiltonians and the definition of the linearized renormalization group 132
8. The linearized renormalization group and its spectrum in the case of Gaussian scaling distributions 134
9. Bifurcation points, non-Gaussian scaling distributions, e-expansions 143
Historical notes and references to Chapter IV 148
Epilogue 150
References 152
Index 158
Other Title in Series 160
| Erscheint lt. Verlag | 20.5.2014 |
|---|---|
| Sprache | englisch |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Thermodynamik |
| Sozialwissenschaften ► Politik / Verwaltung | |
| ISBN-10 | 1-4831-5849-7 / 1483158497 |
| ISBN-13 | 978-1-4831-5849-5 / 9781483158495 |
| Haben Sie eine Frage zum Produkt? |
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