1 Introduction Problems 2 Survey of Equilibrium Critical Phenomena 2.1 Phase Transitions in Equilibrium Systems 2.1.1 Notations 2.1.2 Phase Transitions in Ferromagnetic Systems 2.1.3 Power-law Scaling 2.2 Scale-Invariance and Universality 2.2.1 Scale-Invariance 2.2.2 Scaling Functions and Data Collapses 2.2.3 Universality Classes 2.2.4 Experimental Evidence of Universality 2.3 Mean-Field and Renormalisation Group Methods 2.3.1 Mean-Field Theory of Ferromagnetic Systems 2.3.2 Universal Amplitude Ratios 2.3.3 Remarks on Renormalisation-Group Theory 2.3.4 Scaling Laws Induced by Renormalisation-Group Theory 2.3.5 Field-Theory and c-Expansion 2.3.6 Surface Critical Phenomena 2.3.7 Finite-Size Scaling 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 3.2.1 Basic Scaling Behaviour 3.2.2 Universality and the DP Conjecture 3.2.3 Simple Mean-Field Approximation 3.2.4 Phenomenological Langevin Equation 3.2.5 Update Schemes and Evolution Equations 3.3 Lattice Models of Directed Percolation 3.3.1 Domany-Kinzel Automaton 3.3.2 Contact Process 3.3.3 Pair-Contact Process 3.3.4 Threshold Transfer Process 3.3.5 Ziff-Gulari-Barshad Model 3.3.6 Further Non-equilihrium Phenomena Related to DP 3.4 Experiments Related to Directed Percolation 3.4.1 Experiments Resembling DP Dynamics 3.4.2 Growth Processes Related to DP 3.4.3 Intermittent Turbulence 3.4.4 Discussion Problems 4 Scaling Properties of Absorbing Phase Transitions 4.1 Scaling in the Steady-State 4.1.1 Order Parameters 4.1.2 Rapidity-Reversal Symmetry of Directed Percolation 4.1.3 The Correlation Lengths �Ρ� and �ΨO�O 4.1.4 Scale-Invariance 4.1.5 Two-Point Correlation Function in the Steady-State 4.1.6 Empty-Interval Probabilities in the Steady-State 4.1.7 The External Field h 4.1.8 Fluctuations of the Order-Parameter in the Steady-State 4.1.9 Finite-Size Scaling in the Steady-State 4.2 Dynamical Scaling Behaviour 4.2.1 Homogeneously Active Initial State 4.2.2 Pair-Connectedness Function, I 4.2.3 Spreading Profile at Criticality 4.2.4 Clusters Generated from a Single Seed 4.2.5 Properties of Clusters in the Absorbing Phase 4.2.6 Palr-Connectedness Function, II 4.2.7 Response Function 4.2.8 Early-Time Behaviour and Critical Initial Slip 4.2.9 Fractal Initial Conditions 4.2.10 Influence of an External Field 4.2.11 Finite-Size Scaling 4.2.12 Universality of Finite-Size Amplitudes 4.3 Methods of Analysis 4.3.1 Exact Diagonalisation 4.3.2 Yang-Lee and Fisher Zeros 4.3.3 Series Expansion 4.3.4 Field-Theoretical Methods 4.3.5 Methods for Exact Solution 4.3.6 Monte Carlo Simulations 4.3.7 Universal Moment Ratios 4.3.8 Density-Matrix Renormalisation-Group Methods 4.4 Other Critical Properties 4.4.1 Surface Critical Behaviour 4.4.2 Persistence Exponents Problems 5 Universality Classes Different from Directed Percolation 5.1 Parity-Conserving Universality Class 5.2 Voter Universality Class 5.2.1 The Classical Voter Model 5.2.2 Voter-Type Phase Transitions 5.3 Compact Directed Percolation 5.4 Tricritical Directed Percolation 5.4.1 Mean-Field Approximation of TDP 5.4.2 Numerical Simulations of TDP 5.5 Dynamical Percolation 5.6 Long-Range Interactions 5.6.1 DP with Spatial Levy Flights 5.6.2 DP with Temporal Long-Range Interactions 5.6.3 Other Models with Long-Range Interactions by Levy Flights 5.6.4 Simulating Models with Long-Range Interactions 5.7 Manna Universality Class 5.7.1 Manna Model 5.7.2 Conserved Threshold Transfer Process (CTTP) 5.7.3 Conserved Lattice Gas (CLG) and Other Reaction-Diffusion Processes 5.7.4 Scaling Properties 5.7.5 Relationship Between Absorbing Phase Transitions and Self-Organised Criticality (SOC) 5.7.6 Absorbing Phase Transitions and SOC: Mean-Field Approximation 5.7.7 Relating Critical Exponents of SOC and Absorbing Phase Transitions 5.8 Pair-Contact Process with Diffusion 5.9 First-Order Phase Transitions 5.9.1 Stabilisation by Elimination of Minority Islands 5.9.2 First-Order Transitions in One Spatial Dimension 5.9.3 Impossibility of Discontinuous Phase Transitions in Fluctuating One-Dimensional Systems 5.9.4 Phase Coexistence and Hysteresis Cycles 5.10 Crossover Phenomena 5.10.1 Crossover from DP to TDP 5.10.2 Crossover from DP to CDP 5.10.3 Crossover to Mean-Field Scaling Behaviour 5.11 Quenched Disorder 5.11.1 Temporally Quenched Disorder 5.11.2 Spatially Quenched Disorder 5.12 Attempts of Classification 5.13 Some Open Questions 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 for Absorbing Phase Transitions 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 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 H Fractal Dimensions Solutions Frequently Used Symbols Abbreviations References List of tables List of figures Index