Monte Carlo Simulation

The first simulation technique we will study is the Monte Carlo method. The primary “flavor” of MC most appropriate for this introductory level course is the original Metropolis method, explained in Sec. 3.1.

We will also use MC to explain basic technical aspects of molecular simulation code in Sec. 3.3. These aspects are not all restricted to MC, but following the text, we will introduce and discuss these technical aspects here. These include (1) periodic boundary conditions, (2) energy evaluation, (3) representation of data, among others.

Finally, four case studies will be presented and investigated. The first is the Ising magnet (Sec. 3.2). The second considers hard-disks confined in a circle (Sec. 3.4), and the third is hard-disk-dumbbells (Sec. 3.5). The fourth is MC to explore the equation of state of a model liquid known as the Lennard-Jones fluid (Sec. 3.6).