Elements of a Continuous-Space MC program

The Ising system serves us well as a simple introduction to the technique of Monte Carlo simulation. Now, we move on to the more advanced case of continuous-space Monte Carlo; that is, Monte Carlo on a system composed of particles whose position and velocity vector components are real numbers. We will first consider the simple case of a “hard-sphere” liquid, and then the more realistic Lennard-Jones liquid. These distinctions have to do with the potential energy function used to compute the potential energy ${U}$ of a configuration ${\bf r}^N$.

Regardless of the potential used, all continuous-space MC programs have common elements:

1. data representation and input/output;
2. energy calculation;
3. trial move generation.