Phase Transitions and Critical Phenomena (eBook)

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2000 | 1. Auflage
320 Seiten
Elsevier Science (Verlag)
978-0-08-053875-4 (ISBN)

Infos

The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. No longer an area of specialist interest, it has acquired a central focus in condensed matter studies. The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.
The two review articles in this volume complement each other in a remarkable way. Both deal with what might be called the modern geometric
approach to the properties of macroscopic systems. The first article by Georgii (et al.) describes how recent advances in the application of
geometric ideas leads to a better understanding of pure phases and phase transitions in equilibrium systems. The second article by Alava (et al.)
deals with geometrical aspects of multi-body systems in a hands-on way, going beyond abstract theory to obtain practical answers. The
combination of computers and geometrical ideas described in this volume will doubtless play a major role in the development of statistical
mechanics in the twenty-first century.

Inhalt

Front Cover 1
Phase Transitions and Critical Phenomena 4
Copyright Page 5
Contributors 6
General Preface 8
Preface to Volume 18 10
Contents 12
Chapter 1. The Random Geometry of Equilibrium Phases 18
1 Introduction 20
2 Equilibrium phases 23
3 Some models 31
4 Coupling and stochastic domination 38
5 Percolation 48
6 Random-cluster representations 64
7 Uniqueness and exponential mixing from non-percolation 89
8 Phase transition and percolation 108
9 Random interactions 129
10 Continuum models 140
Acknowledgments 146
References 146
Chapter 2. Exact Combinatorial Algorithms: Ground States of Disordered Systems 160
1 Overview 162
2 Basics of graphs and algorithms 165
3 Flow algorithms 175
4 Matching algorithms 192
5 Mathematical programming 198
6 Percolation and minimal path 203
7 Random Ising magnets 213
8 Line, vortex and elastic glasses 251
9 Rigidity theory and applications 281
10 Closing remarks 312
Acknowledgments 314
References 314
Subject index 335

Produkt-Details

• Erscheint lt. Verlag: 15.9.2000
• Mitarbeit: Herausgeber (Serie): Cyril Domb, Joel L. Lebowitz
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-053875-4 / 0080538754
• ISBN-13: 978-0-08-053875-4 / 9780080538754