The Optimum Maximum Allowed Displacement in Monte Carlo Simulation of Lennard-Jones Potential Point Particles

In this paper, periodic systems of N point particles with Lennard-Jones potential are simulated in three dimensional space using Monte Carlo technique. The maximum allowed displacement used in Monte Carlo simulation of any N-particle system controls the convergence of the calculated potential energy to its physical situation. The optimum maximum allowed displacement associated with 50% acceptance rate is found. Since Lennard-Jones potential is a short range one, it is considered to be zero beyond some cut-off radius. The optimum dimensionless cut-off radius in the Lennard-Jones case is 2.5, which is used in simulations. An explicit mathematical formula for the optimum maximum allowed displacement as a function of both temperature and density is obtained. This formula is predicted by fitting the Monte Carlo results using the fitting tools in Matlab.