Non-Equilibrium Phase Transitions: Volume 2: Ageing and Dynamical Scaling Far from Equilibrium

ISBN-13: 9789048128686 / Angielski / Twarda / 2010 / 544 str.

Malte Henkel;Michel Pleimling

Opis

Dynamical scaling is key to our understanding of far from equilibrium relaxation. Where Volume 1 of this set covered the statics and dynamics of transitions into an absorbing state, this one treats relaxation phenomena far from equilibrium and ageing.

Recenzje

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)

Spis treści

Volume II: 1. Ageing Phenomena 1.1 Introduction 1.2 Phase-Ordering Kinetics 1.3 Phenomenology of Ageing 1.4 Scaling Behaviour of Intergrated Responses 1.5 Values of Non-Equilibrium Exponents 1.6 Global Persistence 2. Exactly Solvable Models 2.1 One-dimensional Glauber-Ising Model 2.2. A Non-Glauberian Kinetic Ising Model 2.3 The Free Random Walk 2.4 The Spherical Model 2.5 The Long-range Spherical Model 2.6 XY-Model in Spin-wave Approximation 2.7 OJK Approximation 2.8 Further Solvable Models 3. Simple Ageing: an Overview 3.1 Non-equilibrium Critical Dynamics 3.2 Ordered Initial States 3.3 Conserved Order-parameter (Model B) 3.4 Fully Frustrated Systems 3.5 Disordered Systems I: Ferromagnets 3.6 Disordered Systems II: Critical Glassy Systems 3.7 Surface Effects 3.8 Ageing with Absorbing Steady-states I 3.9 Ageing with Absorbing Steady-states II 3.10 Reversible Reaction-diffusion Systems 3.11 Growth processes 4. Local scale invariance I: z = 2 4.1 Introduction 4.2 The Schrödinger Group 4.3 From Schrödinger-invariane to Ageing 4.4 Conformal Invariance and Ageing 4.5 Galilei-invariance 4.6 Calculation of Two-time Response and Correlation Functions 4.7 Tests of Ageing and Conformal-invariance for z = 2 4.8 Nonrelativistic AdS/CFT Correspondence 5. Local scale invariance II: z ≠ 2 5.1 Axioms of Local Scale-invariance 5.2 Construction of the Infinitesimal Generators 5.3 Generalised Bargman Superselection Rule 5.4 Calculation of Two-time Responses 5.5 Calculation of Two-time Correlations 5.6 Tests of Local Scale-invariance with z ≠ 2 5.7 Global Time-reparametrisation-invariance 5.8 Concluding Remarks 6. Lifshitz Points 6.1 Phenomenology 6.2 Critical Exponents at Lifshitz Points 6.3 A Different Type of Local Scale-transformation 6.4 Application to Lifshitz Points 6.5 Conclusions 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 Hilhorst-van Leeuven Model A.10 Frustrated Spin Models A.11 Weakly random Spin Systems A.12 Logarithmic Sub-scaling Exponents A.13 Ising Spin Glasses A.14 Gauge Glasses D. Langevin Equations and Path Integrals I. Cluster Algorithms: Competing Interactions J. Fractional Derivatives J.1 Singular Fractional Derivatives J.2 Fractional Laplacians K. Conformally Invarioant Interacting Fields K.1 Conformal Invariance and Coupling Constants K.2 Conformally Conserved Currents L. Lie Groups and Lie Algebras: a Reminder L.1 Finite Groups L.2 Continuous Groups and Lie groups L.3 From Lie groups to Lie Algebras and Back L.4 Matrix Representations and the Cartan-Weyl Basis L.5 Function-space Representations L.6 Central Extensions Solutions. Frequently Used Symbols. Abbreviations. References. List of Tables. List of Figures. Index

O autorze

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.

Blurb

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.