Monte Carlo simulations of disordered systems / S. Jain.

Includes bibliographical references (pages 170-172) and index.

Print version record.

PREFACE; CONTENTS; Chapter 1 INTRODUCTION; Chapter 2 ELEMENTARY PROBABILITY AND STATISTICS; 2.1 Introduction; 2.2 Probability; 2.3 Random Variable; 2.3.1 Expectation value; 2.3.2 Variance; 2.3.3 Covariance; 2.3.4 Function of a random variable; 2.3.5 Conditional expectation; 2.4 Statistics; 2.4.1 Sample mean; 2.4.2 Sample variance; 2.5 Distribution Functions; 2.5.1 The binomial distribution; 2.5.2 The Gaussian distribution; 2.6 Central Limit Theorem; 2.7 Markov Processes; 2.8 Random Numbers; Chapter 3 NUMERICAL INTEGRATION; 3.1 Introduction; 3.2 The Rectangular Rule.

3.3 The Trapezoidal Rule3.4 Simpson's Rule; 3.5 Quadrature Rules; 3.6 The Simple Monte Carlo Technique; 3.7 Hit or Miss Monte Carlo Method; 3.8 The Mixed Method; 3.9 Selective Sampling By Monte Carlo; 3.10 Buffon's Needle; Chapter 4 THERMODYNAMICS; 4.1 Introduction; 4.2 The Laws of Thermodynamics; 4.2.1 The zeroth law of thermodynamics; 4.2.2 The first law of thermodynamics; 4.2.3 The second law of thermodynamics; 4.2.4 The third law of thermodynamics; 4.3 Thermodynamic Relations; 4.4 Response and Correlation Functions; 4.5 Phase Transitions; 4.6 Order Parameters.

4.7 Critical Point Exponents4.8 Ginzburg-Landau Phenomenological Theory of Ferromagnetism; Chapter 5 STATISTICAL MECHANICS; 5.1 Introduction; 5.2 The Microscopic Model; 5.2.1 The classical microscopic model; 5.2.2 The quantum mechanical model; 5.3 Ensembles in Statistical Mechanics; 5.3.1 The Gibbs microcanonical ensemble; 5.3.2 The canonical ensemble; 5.3.3 The grand canonical ensemble; 5.4 Statistical Thermodynamics; 5.5 The Classical Canonical Partition Function; 5.6 Phase Transitions and Critical Exponents; Chapter 6 MODEL SYSTEMS; 6.1 Introduction; 6.2 Basic Model Systems.

6.2.1 Spatial dimensionality6.2.2 Spin dimensionality; 6.2.3 Interactions; 6.2.4 A typical model system; 6.3 An Exactly Solved Model; 6.4 Mean Field Theory; 6.5 Fluctuations; 6.6 Scaling and Scaling Laws; 6.7 Approximate Techniques; Chapter 7 DISORDERED MODEL SYSTEMS; 7.1 Introduction; 7.2 Disorder; 7.2.1 Annealed disorder; 7.2.2 Quenched disorder; 7.3 Disordered Lattices; 7.3.1 Site percolation; 7.3.2 Bond percolation; 7.4 Diluted Spin Systems; 7.4.1 Site-diluted; 7.4.2 Bond-diluted; 7.5 Disordered Interactions; 7.6 Mixed Systems; 7.7 Fractals.

7.7.1 Non-random fractals7.7.2 Random fractals; Chapter 8 MONTE CARLO SIMULATIONS; 8.1 Introduction; 8.2 The Monte Carlo Technique; 8.2.1 Importance sampling; 8.2.2 The transition probability; 8.2.3 The master equation; 8.3 The Two-Dimensional Ising Model; 8.3.1 The algorithm; 8.4 Errors; 8.4.1 Statistical errors; 8.4.2 Systematic errors; 8.5 Further Checks on the Simulations; 8.6 Statistical Analysis; 8.6.1 The chi-squared test; 8.7 Final Note; BIBLIOGRAPHY; INDEX.

This book covers the techniques of computer simulations of disordered systems. It describes how one performs Monte Carlo simulations in condensed matter physics and deals with spin-glasses, percolating networks and the random field Ising model. Other methods mentioned are molecular dynamics and Brownian dynamics. Use of flow-diagrams enables the reader to grasp both the problem and its solution more readily. The book deals with highly complicated problems at a relatively simple level and will be most useful for advanced undergraduate and other courses in computational modelling. Contents: Intr.

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