Phase Transitions and Critical Phenomena Vol 18 1st Edition by Cyril Domb, Joel Lebowitz ISBN 978-0122203183 0122203186

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Product details: 

ISBN 10:  0122203186

ISBN 13: 978-0122203183

Author: Cyril Domb, Joel L. Lebowitz

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 geometricapproach to the properties of macroscopic systems. The first article by Georgii (et al.) describes how recent advances in the application ofgeometric 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. Thecombination of computers and geometrical ideas described in this volume will doubtless play a major role in the development of statisticalmechanics in the twenty-first century.

Table of contents: 

1 The Random Geometry of Equilibrium Phases
H.-O. Georgii, O. Häggström and C. Maes

1 Introduction
2 Equilibrium phases
3 Some models
4 Coupling and stochastic domination
5 Percolation
6 Random-cluster representations
7 Uniqueness and exponential mixing from non-percolation
8 Phase transition and percolation
9 Random interactions
10 Continuum models
11 Acknowledgments
12 References

2 Exact Combinatorial Algorithms: Ground States of Disordered Systems
M. J. Alava, P. M. Duxbury, C. F. Moukarzel and H. Rieger

13 Overview
14 Basics of graphs and algorithms
15 Flow algorithms
16 Matching algorithms
17 Mathematical programming
18 Percolation and minimal path
19 Random Ising magnets
20 Line, vortex and elastic glasses
21 Rigidity theory and applications
22 Closing remarks
23 Acknowledgments
24 References

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Tags: Cyril Domb, Joel Lebowitz, Phase Transitions, Critical Phenomena