1 Ageing Phenomena
1.1 Introduction
1.1.1 Ageing in Mechanically Deformed Polymers
1.1.2 Correlations and Responses
1.1.3 Ageing in Spin Glasses
1.1.4 Ageing in Simple Magnets
1.1.5 Mean-field Theory
1.1.6 Breaking of the Fluctuation-dissipation Theorem: Experiments
1.1.7 Breaking of the Fluctuation-dissipation Theorem: Two Simple Solvable Models
1.1.8 Outline
1.2 Phase-ordering Kinetics
1.2.1 Linear Stability Analysis
1.2.2 Domain Walls
1.2.3 The Allen-Cahn Equation
1.2.4 Topological Defects
1.2.5 Porod's Law
1.2.6 Bray-Rutenberg Theory for the Growth Law
1.2.7 Exact Result in Two Dimensions
1.2.8 Conserved Order-parameter: Phase-separation
1.2.9 Critical Dynamics
1.3 Phenomenology of Ageing
1.3.1 Scaling Forms
1.3.2 Passage into the Ageing Regime
1.3.3 Kurchan's Lemma
1.3.4 The Yeung-Rao-Desai Inequalities
1.4 Scaling Behaviour of Integrated Responses
1.4.1 Thermoremanent Susceptibility
1.4.2 Zero-field Cooled Susceptibility
1.4.3 Intermediate Susceptibility
1.4.4 Alternating Susceptibility
1.5 Values of Non-equilibrium Exponents
1.5.1 Values of the Ageing Exponents a and b
1.5.2 Values of the Critical Autocorrelation Exponent
1.5.3 Values of the Autocorrelation Exponent Below Tc
1.5.4 Values of the Autorespouse Exponent
1.6 Global Persistence
Problems
2 Exactly Solvable Models
2.1 One-dimensional Glauber-Ising Model
2.1.1 Two-time Correlation Function
2.1.2 Two-time Response Function
2.1.3 Low-temperature Initial States
2.1.4 Comparison With the 1D GinzburgoLandau Equation
2.2 A Non-Glauberian Kinetic Ising Model
2.2.1 Definition
2.2.2 Calculation of the Dynamical Exponent
2.2.3 Global Response Functions
2.2.4 Global Correlation Functions
2.3 The Free Random Walk
2.4 The Spherical Model
2.4.1 Definition and Formalism
2.4.2 Solution of the Volterra Integral Equation
2.4.3 Dynamical Scaling Behaviour
2.5 The Long-range Spherical Model
2.5.1 Definition and Composite Observables
2.5.2 Long-range Initial Correlations
2.5.3 Magnetised Initial State
2.6 XY Model in Spin-wave Approximation
2.6.1 Outline of the Method and Applicability
3 Simple Ageing: an Overview
4 Local Scale-invariance I: z ＝ 2
5 Local Scale-invariance II: z ≠ 2
6 Lifshitz Points: Strongly Anisotropic Equilibrium Critical Points
Appendices
Solutions
Frequently Used Symbols
Abbreviations
References
List of Tables
List of Figures
Index
