Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems

Preface 

1 Cellular disorder 
1.1 Perfect spatial order 
1.2 Substitutional disorder 
1.3 Magnetic disorder 
1.4 Ice disorder 
1.5 Short-range order 
1.6 Long-range order 
1.7 The range of order and ordered domains 
1.8 Spectral disorder 

2 Topological disorder 
2.1 Atomicity 36 
2.2 Disordered linear chains 39 
2.3 Physical realizations of one-dimensional systems 43 
2.4 Dimensionality and order 47 
2.5 Dislocation disorder 51 
2.6 .rv1icrocrystalline disorder 56 
2.7 Atomic distribution functions 58 
2.8 Bond network disorder 64 
2.9 Amorphous or paracrystalline? 67 
2.10 Statistical geometry of bond networks 72 
2.11 The Bernal model of a liquid 77 
2.12 Analytical theories of the liquid state 87 
2.13 Liquid mixtures 96 
2.14 Liquid phases of non-spherical molecules 102 
2.15 Gas-like disorder 106 

3 Continuum disorder 
3.1 Continuum models 108 
3.2 Homogeneous random fields 110 
3.3 Ga ussian randomness 113 
3.4 Statistical topography 118 

4 The observation of disorder 
4.1 Diffraction experiments and diffraction theory 122 
4.2 Neutron diffraction 127 
4.3 Structure determination by X-rays 129 
4.4 Small-angle scattering 129 
4.5 Diffraction by a mixture 133 
4.6 Diffraction effects of substitutional disorder 137 
4.7 Diffraction and imaging 140 

5 Statistical mechanics of substitutional disorder 
5.1 Physical problems and mathematical puzzles 142 
5.2 Mean field approximation 144 
5.3 Short-range order 147 
5.4 Cluster methods 151 
5.5 The Ising model in one dimension 161 
5.6 The one-dimensional Heisenberg model 165 
5.7 The Onsager solution of the two-dimensional I sing problem 171 
5.8 Ferroelectric models in two dimensions 178 
5.9 The spherical model of ferromagnetism 182 
5.10 Graphical expansions 187 
5.11 Order as a thermodynamic variable 197 
5.12 Scaling and renormalization of critical phenomena 200 

6 Thermodynamics of topological disorder 
6.1 The linear gas-liquid--crystal 209 
6.2 The van der Waals approximation 213 
6.3 The Percus- Y evick approximation 218 
6.4 Perturbation methods 220 
6.5 The virial series 223 
6.6 Computer sin1ulation methods 226 
6.7 Melting 232 
6.8 Entropy and free volume 240 

7 Macromolecular disorder 
Regular solutions 
Entropy of macromolecular solutions 
Model chains 
Random coils 
Branching and gel formation 
Rubber elasticity 
Excluded volume 
Random walks on a lattice 
Continuum models 
Entanglements 

8 Excitations on a disordered linear chain 
Dynamical, magnetic and electronic excitations 
One-dimensional models 
Phase-angle representation 
Spectral gaps in disordered chains 
The spectral density 
Local density approximation 
Localization of eigenfunctions

9 Excitations on a disordered lattice 
9.1 The TBA model 
9.2 The Green function formalism 
9.3 Propagator and locator expansions 
9.4 The coherent potential approximation 
9.5 Local environment corrections to CPA 
9.6 Spectral bounds and band tails 
9.7 Spectral moments and continued fractions 
9.8 Off-diagonal disorder 
9.9 Anderson localization 
9.10 Percolation theory 
9.11 Maze conduction 

10 Electrons in disordered metals 
10.1 The NFE model 
10.2 Screened pseudopotentials 
10.3 Muffin-tin potentials 
10.4 The electron spectrum 
10.5 Many-atom scattering 
10.6 Scattering operators 
10.7 Partial-wave representations 
10.8 The coherent-wave approximation 
10.9 Cluster scattering 
10.10 Transport theory 

11 Excitations of a topologically disordered network 
11.1 Dynamics of liquids and glasses 
11.2 The continuum limit 
11.3 Ideal tetrahedral coordination 
11.4 Tree models 
11.5 The band-gap paradox 

12 Dilute and amorphous magnets 
12.1 The dilute Ising model 
12.2 Dilute Heisenberg magnets 
12.3 Amorphous ferromagnets and spin glasses

13 Electrons in 'gases' 
13.1 Gas-like disorder 
13.2 The metal-insulator transition 
13.3 Hopping conduction 
13.4 Semi-classical electrons in a random potential 
13.5 Spectral tails in a choppy random potential 

References 

Index