An important application for computer simulations is the calculation of thermodynamic averages in an equilibrium system. We discuss two different examples. In the first case the classical equations of motion are solved for a system of particles interacting pairwise by Lennard-Jones forces (Lennard-Jones fluid). The thermodynamic average is taken along the trajectory, i.e. over the calculated coordinates at different times. The inner virial is compared to the virial expansion of the Lennard-Jones system. The pair distance distribution function characterizes the order of the system. Velocity auto-correlation function and mean square displacement are compared with the Brownian model of diffusive motion.
In the second case the Metropolis method is applied to a one- or two-dimensional system of interacting spins (Ising model). The thermodynamic average is taken over a set of random configurations. The average magnetization in a magnetic field and the phase transition to the ferromagnetic state are compared with analytical expressions.
KeywordsIsing Model Average Magnetization Random Configuration Brownian Model Berendsen Thermostat
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