Monte carlo studies of two-dimensional commensurate-incommensurate transitions

A Monte Carlo study has been made of commensurate-incommensurate behaviour for Lennard-Jones particles on a square commensurate lattice. For a fixed barrier height a pronounced minimum is found in plots of R, the mean distance of the particles from the nearest commensurate site, against ε^*, where ε^* is the depth of the potential well. The initial fall in R with increase in ε^* is shown to be associated with the repulsive part of the inter-particle interaction.