Non-Equilibrium Phase Transitions – Volume 1: Absorbing Phase Transitions – Malte Henkel, Haye Hinrichsen and Sven Lübeck
This book is volume 1 of a two-volume set which describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state. Volume 2 will describe dynamical scaling in far-from-equilibrium relaxation behaviour and ageing.
The book 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.
Series: Theoretical and Mathematical Physics
2009, IV, 454 p., Hardcover
ISBN: 978-1-4020-8764-6 £76
Volume 2: Dynamical Scaling far from Equilibrium, by Prof. Malte Henkel and Dr Michael Pleimling is due for publication late 2009.
Volume 2 (Dynamical Scaling far from Equlibrium) will treat relaxation phenomena far from equilibrium and ageing. Motivated initially from experimental results, dynamical scaling has now been recognised as a cornerstone in the modern understanding in far from equilibrium relaxation. Dynamical scaling is systematically introduced, starting from coarsening phenomena, and existing analytical results and numerical estimates of universal non-equilibrium exponents and scaling functions are reviewed in detail.
Recent theoretical work aims to understand if dynamical scaling may be just a part of a larger symmetry, called local scaling. Initially, this was motivated by certain analogies with the conformal invariance of equilibrium phase transitions but only recently, this work reached a certain completion and this research is presented, systematically and in detail, in book form for the first time.
Quite similar ideas apply to the phase transitions of equilibrium systems with competing interactions and interesting physical realisations, for example in Lifshitz points.
