© 2010

Non-Equilibrium Phase Transitions

Volume 2: Ageing and Dynamical Scaling Far from Equilibrium


  • Focusses on simulation methods, scaling arguments and new methods using dynamical symmetries

  • Reviews in detail existing non-perturbative quantitative results on non-equilibrium phase transitions


Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Malte Henkel, Michel Pleimling
    Pages 1-94
  3. Malte Henkel, Michel Pleimling
    Pages 95-140
  4. Malte Henkel, Michel Pleimling
    Pages 141-220
  5. Malte Henkel, Michel Pleimling
    Pages 221-290
  6. Malte Henkel, Michel Pleimling
    Pages 291-336
  7. Malte Henkel, Michel Pleimling
    Pages 337-368
  8. Back Matter
    Pages 369-561

About this book


This book is Volume 2 of a two-volume set describing two main classes of non-equilibrium phase-transitions. This volume covers dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. Motivated initially by experimental results, dynamical scaling has now been recognised as a cornerstone in the modern understanding of 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. Ageing phenomena in glasses, as well as in simple magnets, are paradigmatic examples of non-equilibrium dynamical scaling, but may also be found in irreversible systems of chemical reactions. Recent theoretical work sought to understand if dynamical scaling may be just a part of a larger symmetry, called local scale-invariance. Initially, this was motivated by certain analogies with the conformal invariance of equilibrium phase transitions; this work has recently reached a degree of completion and the research is presented, systematically and in detail, in book form for the first time. Numerous worked-out exercises are included. Quite similar ideas apply to the phase transitions of equilibrium systems with competing interactions and interesting physical realisations, for example in Lifshitz points.


Phase Transition Phase Transitions ageing phenomena book about dynamical scaling far from equilibrium relaxation phenomena local scale invariance non-equilibrium critical dynamics nonequilibrium phase transitions numerical simulation phenomenological scaling theory physical ageing

Authors and affiliations

  1. 1.Groupe de Physique Statistique Département de Physique de la Matière et des MatériauxInstitut Jean Lamour Nancy - UniversitéVandœuvre lès Nancy CedexFrance
  2. 2.Physics DepartmentVirginia Polytechnic Institute & State UniversityBlacksburgUnited States

About the authors

Malte Henkel, born in 1960, received his Master's degree from the University of Bonn in 1984, and his PhD in 1987, when he also won the annual prize of the Minerva Foundation. From that year onward he has been a long-term visitor in many institutes, including the ITP at Santa Barbara, USA, the SPhT at Saclay, France, and the universities of Oxford, UK, Vienna, Austria, Padova, Italy, and Lisbon, Portugal. In 1995 he was appointed a professor at the University of Nancy I. His current research encompasses equilibrium and non-equilibrium phase transitions, using field-theoretical and numerical methods in general. In particular, his current focus is on dynamical scaling behaviour realised in ageing phenomena far from equilibrium. He has published well over a hundred articles and three monographs, one of which is Volume I of this set.

Bibliographic information

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From the reviews:

“This book is the second of a two-volume work on non-equilibrium phase transitions … . a well written and valuable introduction to these problems, for mathematicians as well as for physicists. … The book finishes with several appendices, where the reader can be reminded of useful physical and mathematical results … a large section where the almost one hundred problems proposed throughout the book are fully worked out, and a huge and very useful reference list of more than seven hundred fifty items.” (Fernando Pestana da Costa, Mathematical Reviews, Issue 2011 j)