Monte Carlo Methods In Statistical Physics

Foreword / Preface / Prologue / What is a Monte Carlo Method? / Generation of a Sequence of Pseudo Random Numbers / How Do We Know a Sequence of Numbers is Random / Random Sampling Techniques / Monte Carlo Integration / Basic Principle of Importance Sampling / Using Spin Model / How do we Simulate an Using Spin System? / Markov Chain / Metropolis Algorithm / Monte Carlo Averages and Error Bars / How Does an Using Spin System Behave in the Vicinity of Phase Transition? / Finite Size Scaling / What is the n-fold Way? / Critical Slowing Down / Error Bars from Correlated Data: Blocking Technique / What is Percolation? / Swendsen-Wang Algorithm / Hoshen-Kopelman Cluster Counting Algorithm / What are the Improvements to the Swendsen-Wang Cluster Algorithm? / Histogram Technique / Entropic or Multicanonical Sampling / Wang-Landau Algorithm / Jarzynski's Equality / Epilogue / Appendix / References / Index

Monte Carlo simulation is a computer-based numerical technique that has gained popularity in the recent times in physical sciences due to its ability to extract real world observations out of seemingly intractable theoretical models. In fact, Monte Carlo simulation may be regarded as the new and third major arm of investigations in the physical sciences, the other two traditional being Experiment and Theory. It is an important tool in Computational Methods, particularly so in Statistical Physics for relating macroscopic observations to the laws of microscopic world. In this book, the author elucidates the methodology of Monte Carlo technique starting from the very beginning, and leads the reader to a level where he/she can take it up for serious research projects. Enough background material has been provided to make the text self-contained; there are several simple examples from Physics that lucidly illustrate the concept. The style of presentation is informal yet informative, and conceptual complexity has been handled in a user-friendly manner without sacrificing logical rigour. A serious student should find the presentation absorbing and educative.