Non-Equilibrium Phase Transitions: Volume 1: Absorbing Phase Transitions

ISBN-13: 9781402087646 / Angielski / Twarda / 2009 / 404 str.

Malte Henkel; Haye Hinrichsen; Sven La1/4beck

Opis

"The career structure and funding of the universities . . . ] currently strongly d- courages academics and faculties from putting any investment into teaching - there are no career or ?nancial rewards in it. This is a great pity, because . . . ] it is the need toengage indialogue, and to makethings logicaland clear, that istheprimary defence against obscurantism and abstraction. " B. Ward-Perkins, The fall of Rome, Oxford (2005) This is the ?rst volume of a planned two-volume treatise on non-equilibrium phase transitions. While such a topic might sound rather special and a- demic, non-equilibrium critical phenomena occur in much wider contexts than their equilibrium counterparts, and without having to ?ne-tune th- modynamic variables to their 'critical' values in each case. As a matter of fact, most systems in Nature are out of equilibrium. Given that the theme of non-equilibrium phase transitions of second order is wide enough to amount essentially to a treatment of almost all theoretical aspects of non-equilibrium many-body physics, a selection of topics is required to keep such a project within a manageable length. Therefore, Vol. 1 discusses a particular kind of non-equilibrium phase transitions, namely those between an active, ?- tuating state and absorbing states. Volume 2 (to be written by one of us (MH) with M. Pleimling) will be devoted to ageing phenomena.

Recenzje

From the reviews:

"The monograph concentrates on nonequilibrium phase transitions from fluctuating (ordered) states into so-called absorbing states, which can never be left by the system once reached. ... Extended appendices (plus solutions of excercises and answers to problems) on specific models ... make the book useful not only to scientists and lecturers, but also to advanced graduate students." (Piotr Garbaczewski, Zentralblatt MATH, Vol. 1165, 2009)

"This research monograph ... provides a highly desirable and topical pedagogical introduction as well as a timely overview of recent advances in theoretical investigations of continuous non-equilibrium phase transition from active states to inactive absorbing states. ... This text is likely to become a standard reference in the field, and should be an indispensable source of information for both beginning and already seasoned researchers interested in non-equilibrium statistical physics, the theory of stochastic processes, and fundamental properties of reaction-diffusion systems ... ." (Uwe C. Täuber, Mathematical Reviews, Issue 2012 h)

Spis treści

1 Introduction. Problems.
2 Survey of Equilibrium Critical Phenomena 2.1 Phase Transitions in Equilibrium Systems 2.2 Scale Invariance and Universality 2.3 Mean-field and Renormalisation Group Methods 2.4 Fluctuation-dissipation Theorem 2.5 From Scale-invariance to Conformal Invariance. Problems.
3 Directed percolation 3.1 Directed Percolation at First Glance 3.2 Directed Percolation as a Stochastic Process 3.3 Lattice Models of Directed Percolation 3.4 Experiments related to Directed Percolation. Problems.
4 Scaling Properties of Absorbing Phase Transitions 4.1 Scaling in the Steady State 4.2 Dynamical Scaling Behaviour 4.3 Methods of Analysis 4.4 Other Critical Properties. Problems.
5 Universality classes different from directed percolation 5.1 Parity-Conserving Universality Class 5.2 Voter Universality Class 5.3 Compact Directed Percolation 5.4 Tricritical Directed Percolation 5.5 Dynamical Percolation 5.6 Long-range Interactions 5.7 Manna Universality Class 5.8 Pair Contact Process with Diffusion 5.9 First-order Phase Transitions 5.10 Crossover Phenomena 5.11 Quenched Disorder. Problems.
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.

Blurb

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.