# Metropolis Monte Carlo Models

The Lennard-Jones Metropolis model uses the Metropolis Monte Carlo algorithm to simulate n particles interacting through the Lennard-Jones potential. A Monte Carlo method is a stochastic (nondeterministic) algorithm that uses random numbers to sample an ensemble. The canonical ensemble is a large number number of systems with the same temperature each of which represents a possible state of the actual system. Although the temperature of the cannonical ensemble is constant, the energy of a system in the ensemble is not.

Simple Monte Carlo methods become inefficient (or fail) if they do not sample all possible configurations (phase space). The Lennard-Jones Metropolis model shows snapshots of phase space sampled by the Metropolis algorithm. Do the snapshots in this simulation suggest that phase space is being sampled correctly at high temperature? Low temperature?

### Related Models

See the Lennard-Jones Demon model for similar model that uses the demon algorithm.

### Note:

This simulation was created by Wolfgang Christian using the Easy Java Simulations (Ejs) modeling tool. You can modify this simulation if you have Ejs installed by right-clicking within a plot and selecting "Open Ejs Model" from the pop-up menu. Information about Ejs is available at: <http://www.um.es/fem/Ejs/>.