The Optimum Maximum Allowed Displacement in Monte Carlo Simulation of Lennard-Jones Potential Point Particles = الحد الأقصى الأمثل للنزوح المسموح به في محاكاة مونت كارلو لجزيئات لينار جونز النقطية

Abstract

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 Nparticle 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.