Monte Carlo Simulation and Integration

This chapter contains sections titled: Introduction and Fundamentals Some Historical Remarks Random Numbers Random Walk Simulation Hit-or-Miss Random Sampling Integration Simple or Naive Sampling — Nonweighted Monte Carlo Integration Importance Sampling — Weighted Monte Carlo Integration The Metropolis Monte Carlo Method Fundamentals of the Algorithm The Metropolis Method for Canonical and Microcanonical Ensembles The Metropolis Method for Grandcanonical Ensembles Spin Monte Carlo Models Introduction ½ Spin Ising Model Heisenberg Spin Model Lattice Gas Spin Model q-State Potts Spin Model Ising-Related Spin Models — the MFA, CVM, and BWG Models Lattice Types Errors of Monte Carlo Methods Application of the Monte Carlo Method in Materials Science Examples of the Monte Carlo Method in Materials Science Simulation of Surface Segregation Simulation of Phase Transition in Polymers Simulation of Thin Film Deposition