Topics in Current Physics

1. A Simple Introduction to Monte Carlo Simulation and Some Specialized Topics.- 1.1 A First Guide to Monte Carlo Sampling.- 1.1.1 Random Numbers.- 1.1.2 An Example of "Simple Sampling": The Percolation Problem.- 1.1.3 An Example of "Importance Sampling": The Ising Model.- 1.1.4 An Example of Continuous Degrees of Freedom: The Heisenberg Model.- 1.1.5 A First Warning: Finite-Size Effects, Metastability, Slowing Down.- 1.2 Special Topics.- 1.2.1 What can be Learned from Distribution Functions; Finite-Size Scaling.- 1.2.2 Estimation of Free Energy and Entropy.- 1.2.3 Estimation of Intensive Thermodynamic Quantities.- 1.2.4 Interface Free Energy.- 1.2.5 Methods of Locating First-Order Phase Changes.- 1.2.6 Linear Response, Susceptibilities and Transport Coefficients.- 1.3 Conclusion.- Appendix. 1.A. Multispin Coding.- References.- Notes Added in Proof.- 2. Recent Developments in the Simulation of Classical Fluids.- 2.1 Some Recent Methodological Developments.- 2.1.1 Modified Metropolis Algorithms.- 2.1.2 Sampling in the Grand-Canonical Ensemble.- 2.1.3 Evaluation of the Chemical Potential.- 2.1.4 Variations on a Theme.- 2.2 Simple Monatomic Fluids.- 2.2.1 Hard-Core Systems in Two and Three Dimensions.- 2.2.2 Soft-Core and Lennard-Jones Systems in Two Dimensions.- 2.2.3 Rare-Gas Fluids in Three Dimensions.- 2.2.4 Binary Mixtures of Simple Fluids.- 2.3 Coulombic Systems.- 2.3.1 Boundary Conditions.- 2.3.2 The One-Component Plasma (OCP).- 2.3.3 Two-Dimensional Electron Layers.- 2.3.4 Liquid Metals.- 2.3.5 Primitive Model Electrolytes.- 2.3.6 Simple Models of Polyelectrolytes.- 2.3.7 Molten Salts and Superionic Conductors.- a) KCl.- b) KCN.- c) Alkali Chlorides.- d) Rb Halides.- e) Cs Halides.- f) Alkaline Earth Halides.- g) Molten Salt Mixtures.- h) Superionic Conductors.- 2.4 Molecular Liquids.- 2.4.1 Hard Nonspherical Particles.- a) Hard Spherocylinders.- b) Mixtures of Hard Spheres and Hard Spherocylinders.- c) Hard Diatomics.- 2.4.2 Two-Center Molecular Liquids.- 2.4.3 Simple Dipolar and Multipolar Liquids.- a) Dipolar Hard-Sphere Systems.- b) Two- and Three-Dimensional Stockmayer Fluids.- c) Systems of Polarizable Particles.- d) Steric Effects in Polar Fluids.- 2.4.4 Realistic Models of Molecular Liquids.- 2.4.5 Liquid Water.- 2.5 Solutions.- 2.5.1 Dilute Aqueous Solutions of Nonelectrolytes.- 2.5.2 Solvation of Ions.- 2.5.3 Solvation of Large Dipoles.- 2.5.4 Solvation of Biological Molecules.- 2.6 Surfaces and Interfaces.- 2.6.1 Liquid-Vapor Interface of Simple Fluids.- 2.6.2 Liquid-Vapor Interface of Molecular Fluids.- 2.6.3 Density Profiles of the One-Component Plasma and Liquid Metals.- 2.6.4 Liquid-Wall Interfaces.- 2.6.5 Liquid-Solid Coexistence.- 2.6.6 The Electrical Double Layer.- 2.7 Conclusion.- References.- 3. Monte Carlo Studies of Critical and Multicritical Phenomena.- 3.1 Two-Dimensional Lattice-Gas Ising Models.- 3.1.1 Adsorbed Monolayers.- 3.1.2 Ising Model Critical and Multicritical Behavior.- 3.1.3 Models with Incommensurate Phases.- 3.2 Surfaces and Interfaces.- 3.3 Three-Dimensional Binary-Alloy Ising Models.- 3.4 Potts Models.- 3.5 Continuous Spin Models.- 3.6 Dynamic Critical Behavior.- 3.7 Other Models.- 3.7.1 Miscellaneous Magnetic Models.- 3.7.2 Superconductors.- 3.7.3 Interacting Electric Multipoles.- 3.7.4 Liquid Crystals.- 3.8 Conclusion and Outlook.- References.- 4. Few- and Many-Fermion Problems.- 4.1 Review of the GFMC Method.- 4.2 The Short Time Approximation.- 4.3 The Fermion Problem and the Method of Transient Estimation.- 4.4 The Fixed Node Approximation.- 4.5 An Exact Solution for Few-Fermion Systems.- 4.6 Speculations and Conclusions.- References.- 5. Simulations of Polymer Models.- 5.1 Background.- 5.2 Variants of the Monte Carlo Sampling Techniques.- 5.3 Equilibrium Configurations.- 5.3.1 Asymptotic Properties of Single Chains in Good Solvents.- 5.3.2 Phase Transitions of Single Chains.- 5.3.3 Chain Morphology in Concentrated Solutions and in the Bulk.- 5.3.4 Phase Transitions at High Concentrations.- 5.4 Polymer Dynamics.- 5.4.1 Brownian Dynamics of a Single Chain.- 5.4.2 Entanglement Effects.- 5.5 Conclusions and Outlook.- References.- 6. Simulation of Diffusion in Lattice Gases and Related Kinetic Phenomena.- 6.1 General Aspects of Monte Carlo Approaches to Dynamic Phenomena.- 6.2 Diffusion in Lattice-Gas Systems in Equilibrium.- 6.2.1 Self-Diffusion in Noninteracting Two- and Three-Dimensional Lattice Gases.- 6.2.2 Anomalous Diffusion in One-Dimensional Lattices.- 6.2.3 Tracer Particles with Different Jump Rates and the Percolation Conduction Problem.- 6.2.4 Self-Diffusion and Collective Diffusion in Interacting Lattice Gases, Including Systems with Order-Disorder Phase Transitions.- 6.3 Diffusion and Domain Growth in Systems far from Equilibrium.- 6.3.1 Nucleation, Spinodal Decomposition, and Lifshitz-Slyozov Growth.- 6.3.2 Late-Stage Sealing Behavior.- 6.3.3 Diffusion of Domain Walls and Ordering Kinetics.- 6.3.4 Kinetics of Aggregation, Gelation and Related Phenomena.- 6.4 Conclusion.- References.- 7. Roughening and Melting in Two Dimensions.- 7.1 Introductory Remarks.- 7.2 Roughening Transition.- 7.2.1 Solid-on-Solid (SOS) Model.- 7.2.2 Dual Coulomb Gas (CG) Model.- 7.2.3 Step Free Energy and Crystal Morphology.- 7.3 Melting Transition.- 7.3.1 Theoretical Predictions.- 7.3.2 Computer Experiments on Atomistic Systems.- 7.3.3 Dislocation Vector System.- References.- 8. Monte Carlo Studies of "Random" Systems.- 8.1 General Introduction.- 8.2 Spin Glasses.- 8.2.1 Short-Range Edwards-Anderson Ising Spin Glasses.- 8.2.2 Short-Range Edwards-Anderson Heisenberg Spin Glasses.- 8.2.3 Site-Disorder Models.- 8.2.4 The Infinite-Range Model.- 8.2.5 One-Dimensional Models.- 8.3 Other Systems with Random Interactions.- 8.4 Percolation Theory.- 8.4.1 Cluster Numbers.- 8.4.2 Computational Techniques.- 8.4.3 Cluster Structure.- 8.4.4 Large-Cell Monte Carlo Renormalization.- 8.4.5 Other Aspects.- 8.5 Conclusion.- References.- Note Added in Proof.- 9. Monte Carlo Calculations in Lattice Gauge Theories.- 9.1 Lattice Gauge Theories: Fundamental Notions.- 9.2 General Monte Carlo Results for Lattice Gauge Systems.- 9.3 Monte Carlo Determination of Physical Observables.- References.- Additional References with Titles.