Universality in nonequilibrium lattice systems : theoretical foundations / Géza Ódor.

Format:

Book

Author/Creator:

Ódor, Géza.

Language:

English

Subjects (All):

Scaling laws (Statistical physics).

Lattice theory.

Self-organizing systems.

Phase transformations (Statistical physics).

Differentiable dynamical systems.

Physical Description:

xix, 276 pages : illustrations ; 24 cm

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, [2008]

Summary:

Universal scaling behavior is an attractive feature in statistical physics because a wide range of models can be classified purely in terms of their collective behavior due to a diverging correlation length. This book provides a comprehensive overview of dynamical universality classes occurring in nonequilibrium systems defined on regular lattices. The factors determining these diverse universality classes have yet to be fully understood, but the book attempts to summarize our present knowledge, taking them into account systematically.

The book helps the reader to navigate in the zoo of basic models and classes that were investigated in the past decades, using field theoretical formalism and topological diagrams of phase spaces. Based on a review in Rev. Mod. Phys. by the author, it incorporates surface growth classes, classes of spin models, percolation and multi-component system classes as well as damage spreading transitions. (The success of that review can be quantified by the more than one hundred independent citations of that paper since 2004.)

The extensions in this book include new topics like local scale invariance, tricritical points, phase space topologies, nonperturbative renormalization group results and disordered systems that are discussed in more detail. This book also aims to be more pedagogical, providing more background and derivation of results. Topological phase space diagrams introduced by Kamenev (Physical Review E 2006) very recently are used as a guide for one-component, reaction-diffusion systems. Book jacket.

Contents:

1.1 Critical exponents of equilibrium (thermal) systems 1

1.2 Static percolation cluster exponents 2

1.3 Dynamical critical exponents 4

1.4 Crossover between classes 9

1.5 Critical exponents and relations of spreading processes 10

1.5.1 Damage spreading exponents 12

1.6 Field theoretical approach to reaction-diffusion systems 13

1.6.1 Classification scheme of one-component, bosonic RD models, with short ranged interactions and memory 17

1.6.2 Ageing and local scale invariance (LSI) 20

1.7 The effect of disorder 23

2 Out of Equilibrium Classes 27

2.1 Field theoretical description of dynamical classes at and below T[subscript c] 27

2.2 Dynamical classes at T[subscript c] > 0 30

2.3 Ising classes 31

2.3.1 Correlated percolation clusters at T[subscript C] 32

2.3.2 Dynamical Ising classes 33

2.3.3 Competing dynamics added to spin-flip 37

2.3.4 Competing dynamics added to spin-exchange 40

2.3.5 Long-range interactions and correlations 40

2.3.6 Damage spreading behavior 41

2.3.7 Disordered Ising classes 41

2.4 Potts classes 45

2.4.1 Correlated percolation at T[subscript c] 46

2.4.2 The vector Potts (clock) model 47

2.4.3 Dynamical Potts classes 47

2.4.4 Long-range interactions 49

2.5 XY model classes 49

2.5.1 Long-range correlations 51

2.6 O(N) symmetric model classes 52

2.6.1 Correlated percolation at T[subscript c] 53

2.6.2 Disordered O(N) classes 54

3 Genuine Basic Nonequilibrium Classes with Fluctuating Ordered States 55

3.1 Driven lattice gas (DLG) classes 55

3.1.1 Driven lattice gas model in two-dimensional (DDS) 56

3.1.2 Driven lattice gas model in one-dimensional (ASEP, ZRP) 57

3.1.3 Driven lattice gas with disorder 62

3.1.4 Critical behavior of self-propelled particles 63

4 Genuine Basic Nonequilibrium Classes with Absorbing State 65

4.1 Mean-field classes of general nA to (n + k)A, mA to (m - l)A processes 67

4.1.1 Bosonic models 68

4.1.2 Site restricted (fermionic) models 68

4.1.3 The n = m symmetric case 69

4.1.4 The n > m asymmetric case 70

4.1.5 The asymmetric n < m case 71

4.1.6 Upper critical behavior and below 72

4.2 Directed percolation (DP) classes 73

4.2.1 The contact process 81

4.2.2 Two-point correlations, ageing properties 82

4.2.3 DP-class stochastic cellular automata 83

4.2.4 Branching and annihilating random walks with odd number of offspring 87

4.2.5 DP with spatial boundary conditions 87

4.2.6 DP with mixed (parabolic) boundary conditions 91

4.2.7 Levy flight anomalous diffusion in DP 91

4.2.8 Long-range correlated initial conditions in DP 93

4.2.9 Anisotropic DP systems 95

4.2.10 Quench disordered DP classes 95

4.3 Generalized, n-particle contact processes 99

4.4 Dynamical isotropic percolation (DIP) classes 103

4.4.1 Static isotropic percolation universality classes 104

4.4.2 DIP with spatial boundary conditions 106

4.4.3 Levy flight anomalous diffusion in DIP 106

4.5 Voter model (VM) classes 107

4.5.1 The 2A to 0 (ARW) and the 2A to A models 109

4.5.2 Compact DP (CDP) with spatial boundary conditions 111

4.5.3 CDP with parabolic boundary conditions 111

4.5.4 Levy flight anomalous diffusion in ARW-s 112

4.5.5 ARW with anisotropy 114

4.5.6 ARW with quenched disorder 115

4.6 Parity conserving (PC) classes 116

4.6.1 Branching and annihilating random walks with even number of offspring (BARWe) 117

4.6.2 The NEKIM model 122

4.6.3 Parity conserving, stochastic cellular automata 127

4.6.4 PC class surface catalytic models 129

4.6.5 Long-range correlated initial conditions 132

4.6.6 Spatial boundary conditions 133

4.6.7 BARWe with long-range interactions 136

4.6.8 Parity conserving NEKIMCA with quenched disorder 137

4.6.9 Anisotropic PC systems 140

4.7 Classes in models with n < m production and m particle annihilation at [sigma subscript c] = 0 143

4.8 Classes in models with n < m production and m particle coagulation at [sigma subscript c] = 0; reversible reactions (1R) 146

4.9 Generalized PC models 150

4.10 Multiplicative noise classes 152

5 Scaling at First-Order Phase Transitions 155

5.1 Tricritical directed percolation classes (TDP) 159

5.2 Tricritical DIP classes 163

6 Universality Classes of Multi-Component Systems 165

6.1 The A + B to 0 classes 165

6.1.1 Reversible A + A [right harpoon over left] C and A + B [right harppon over left] C class 167

6.1.2 Anisotropic A + B to 0 168

6.1.3 Disordered A + B to 0 models 169

6.2 AA to 0, BB to 0 with hard-core exclusion 169

6.3 Symmetrical, multi-species A[subscript i] + A[subscript j] to 0 (q-MAM) classes 171

6.4 Heterogeneous, multi-species A[subscript i] + A[subscript j] to 0 system 173

6.5 Unidirectionally coupled ARW classes 175

6.6 DP coupled to frozen field classes 176

6.6.1 The pair contact process (PCP) model 178

6.6.2 The threshold transfer process (TTP) 180

6.7 DP with coupled diffusive field classes 182

6.7.1 The PCPD model 184

6.7.2 Cyclically coupled spreading with pair annihilation 188

6.7.3 The parity conserving annihilation-fission model 188

6.7.4 The driven PCPD model 189

6.8 BARWe with coupled non-diffusive field class 190

6.9 DP with diffusive, conserved slave field classes 190

6.10 DP with frozen, conserved slave field classes 193

6.10.1 Realizations of NDCF classes, SOC models 195

6.10.2 NDCF with anisotropy 199

6.10.3 NDCF with spatial boundary conditions 199

6.11 Coupled N-component DP classes 200

6.12 Coupled N-component BARW2 classes 200

6.12.1 Generalized contact processes with n > 2 absorbing states in one dimension 202

6.13 Hard-core 2-BARW2 classes in one dimension 203

6.13.1 Hard-core 2-BARWo models in one dimension 204

6.13.2 Coupled binary spreading processes 205

7 Surface-Interface Growth Classes 209

7.1 The random deposition class 212

7.2 Edwards-Wilkinson (EW) classes 213

7.3 Quench disordered EW classes (QEW) 213

7.3.1 EW classes with boundaries 214

7.4 Kardar-Parisi-Zhang (KPZ) classes 216

7.4.1 KPZ with anisotropy 218

7.4.2 The Kuramoto-Sivashinsky (KS) Equation 219

7.4.3 Quench disordered KPZ (QKPZ) classes 220

7.4.4 KPZ classes with boundaries 221

7.5 Other continuum growth classes 223

7.5.1 Molecular beam epitaxy classes (MBE) 223

7.5.2 The Bradley-Harper (BH) model 225

7.5.3 Classes of mass adsorption-desorption aggregation and chipping models (SOC) 225

7.6 Unidirectionally coupled DP classes 229

7.6.1 Monomer adsorption-desorption at terraces 230

7.7 Unidirectionally coupled PC classes 232

7.7.1 Dimer adsorption-desorption at terraces 233.

Notes:

Includes bibliographical references (pages 249-269) and index.

ISBN:

981281227X

9789812812278

OCLC:

225820401