Non-Equilibrium Phase Transitions

This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.

Brings together for the first time the full range of results known for directed percolation, contact processes and their relatives Uniquely offers a treatment of relaxation phenomena related to ageing Extensive sample problem sets with detailed solutions provided throughout the book Can serve as a standard introductory text for beginning graduate students in this field

Klappentext

This book describes two main classes of non-equilibrium phase-transitions: (a) static and dynamics of transitions into an absorbing state, and (b) dynamical scaling in far-from-equilibrium relaxation behaviour and ageing.

The first volume begins with an introductory chapter which recalls the main concepts of phase-transitions, set for the convenience of the reader in an equilibrium context. The extension to non-equilibrium systems is made by using directed percolation as the main paradigm of absorbing phase transitions and in view of the richness of the known results an entire chapter is devoted to it, including a discussion of recent experimental results. Scaling theories and a large set of both numerical and analytical methods for the study of non-equilibrium phase transitions are thoroughly discussed.

The techniques used for directed percolation are then extended to other universality classes and many important results on model parameters are provided for easy reference.

Inhalt

1 Introduction. 2 Survey of Equilibrium Critical Phenomena. 3 Directed percolation. 4 Scaling Properties of Absorbing Phase Transitions 4.1 Scaling in the Steady State. 5 Universality classes different from directed percolation. Appendices: A Equilibrium Models A.1 Potts model A.2 Clock model A.3 Turban model A.4 Baxter-Wu model A.5 Blume-Capel model A.6 XY model A.7 O(n) model A.8 Double exchange model A.9 Frustrated spin models A.10 Hilhorst-van Leeuven model B Scaling Laws C Diagonalisation of Time-Evolution Operators D Langevin Equations and Path Integrals E Mean-Field Approximations E.1 Simple mean-field/site approximation E.2 Pair-approximation E.3 The 'hop-away' mean-field approximation F On Finite-Size Scaling Techniques F.1 Sequences of finite-size estimates F.2 Sequence extrapolation G Numerical Methods G.1 Simulational techniques G.2 Computation of response functions. Solutions. Frequently Used Symbols. Abbreviations. References. Index.