Advanced Statistical Mechanics GIBBS ENSEMBLE MONTE CARLO SIMULATIONS FOR LENNARD-JONESIUM Summary Write a program to simulate Lennard-Jonesium in the Gibbs-ensemble. Determine the vapor-liquid

The Gibbs phase coexistence rule states that two connected phases are in equilibrium when they are characterized by the same pressure, temperature, and chemical potential (of all species). It is one of the most important goals of computer simulation to understand and predict phase equilibria. Until recently, however, the determination of phase equilibria by simulation was a tedious task and, in the case of vapor-liquid equilibria, involved numerous calculations at different pressures in the isobaric-isothermal ensemble (or different densities in the canonical ensemble) to find a single set of coexistence densities. In 1987, the Gibbs-ensemble Monte Carlo techniques was proposed by Panagiotopoulos [1] which is designed to overcome the limitations of the conventional simulation techniques. Further background on the technique can be found in refs. [2,3].