Synopsis
1. Introduction.- 1.1 General Remarks.- 1.2 Progress in the Understanding of Finite Size Effects at Phase Transitions.- 1.2.1 Asymmetric First-Order Phase Transition.- 1.2.2 Coexisting Phases.- 1.2.3 Critical Phenomena Studies in the Microcanonical Ensemble.- 1.2.4 Anisotropy Effects in Finite Size Scaling.- 1.3 Statistical Errors.- 1.4 Final Remarks.- References.- 2. Vectorisation of Monte Carlo Programs for Lattice Models Using Supercomputers.- 2.1 Introduction.- 2.2 Technical Details.- 2.2.1 Basic Principles.- 2.2.2 Some "Dos" and "Don'ts" of Vectorisation.- 2.3 Simple Vectorisation Algorithms.- 2.4 Vectorised Multispin Coding Algorithms.- 2.5 Vectorised Multilattice Coding Algorithms.- 2.6 Vectorised Microcanonical Algorithms.- 2.7 Some Recent Results from Vectorised Algorithms.- 2.7.1 Ising Model Critical Behaviour.- 2.7.2 First-Order Transitions in Potts Models.- 2.7.3 Dynamic Critical Behaviour.- 2.7.4 Surface and Interface Phase Transitions.- 2.7.5 Bulk Critical Behaviour in Classical Spin Systems.- 2.7.6 Quantum Spin Systems.- 2.7.7 Spin Exchange and Diffusion.- 2.7.8 Impurity Systems.- 2.7.9 Other Studies.- 2.8 Conclusion.- References.- 3. Parallel Algorithms for Statistical Physics Problems.- 3.1 Paradigms of Parallel Computing.- 3.1.1 Physics-Based Description.- (a) Event Parallelism.- (b) Geometric Parallelism.- (c) Algorithmic Parallelism.- 3.1.2 Machine-Based Description.- (a) SIMD Architecture.- (b) MIMD Architecture.- (c) The Connectivity.- (d) Measurements of Machine Performance.- 3.2 Applications on Fine-Grained SIMD Machines.- 3.2.1 Spin Systems.- 3.2.2 Molecular Dynamics.- 3.3 Applications on Coarse-Grained MIMD Machines.- 3.3.1 Molecular Dynamics.- 3.3.2 Cluster Algorithms for the Ising Model.- 3.3.3 Data Parallel Algorithms.- (a) Long-Range Interactions.- (b) Polymers.- 3.4 Prospects.- References.- 4. New Monte Carlo Methods for Improved Efficiency of Computer Simulations in Statistical Mechanics.- 4.1 Overview.- 4.2 Acceleration Algorithms.- 4.2.1 Critical Slowing Down and Standard Monte Carlo Method.- 4.2.2 Fortuin-Kasteleyn Transformation.- 4.2.3 Swendsen-Wang Algorithm.- 4.2.4 Further Developments.- 4.2.5 Replica Monte Carlo Method.- 4.2.6 Multigrid Monte Carlo Method.- 4.3 Histogram Methods.- 4.3.1 The Single-Histogram Method.- 4.3.2 The Multiple-Histogram Method.- 4.3.3 History and Applications.- 4.4 Summary.- References.- 5. Simulation of Random Growth Processes.- 5.1 Irreversible Growth of Clusters.- 5.1.1 A Simple Example of Cluster Growth: The Eden Model.- 5.1.2 Laplacian Growth.- (a) Moving Boundary Condition Problems.- (b) Numerical Simulation of Dielectric Breakdown and DLA.- (c) Fracture.- 5.2 Reversible Probabilistic Growth.- 5.2.1 Cellular Automata.- 5.2.2 Damage Spreading in the Monte Carlo Method.- 5.2.3 Numerical Results for the Ising Model.- 5.2.4 Heat Bath Versus Glauber Dynamics in the Ising Model.- 5.2.5 Relationship Between Damage and Thermodynamic Properties.- 5.2.6 Damage Clusters.- 5.2.7 Damage in Spin Glasses.- 5.2.8 More About Damage Spreading.- 5.3 Conclusion.- References.- 6. Recent Progress in the Simulation of Classical Fluids.- 6.1 Improvements of the Monte Carlo Method.- 6.1.1 Metropolis Algorithm.- 6.1.2 Monte Carlo Simulations and Statistical Ensembles.- (a) Canonical, Grand Canonical and Semi-grand Ensembles.- (b) Gibbs Ensemble.- (c) MC Algorithm for "Adhesive" Particles.- 6.1.3 Monte Carlo Computation of the Chemical Potential and the Free Energy.- (a) Chemical Potential.- (b) Free Energy.- 6.1.4 Algorithms for Coulombic and Dielectric Fluids.- 6.2 Pure Phases and Mixtures of Simple Fluids.- 6.2.1 Two-Dimensional Simple Fluids.- 6.2.2 Three-Dimensional Monatomic Fluids.- 6.2.3 Lennard-Jones Fluids and Similar Systems.- 6.2.4 Real Fluids.- 6.2.5 Mixtures of Simple Fluids.- (a) Hard Core Systems.- (b) LJ Mixtures.- (c) Polydisperse Fluids.- 6.3 Coulombic and Ionic Fluids.- 6.3.1 One-Component Plasma, Two-Component Plasma and Primitive Models of Electrolyte Solutions
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