Size-dependent properties of two-dimensional solids

Abstract

Using Monte Carlo simulations we have found a significant logarithmic size dependence for the density of defects, the shear elastic constant, and the long-range angular order in two-dimensional solids close to their melting points. These size dependencies were present for both hard discs and the repulsive inverse 12th-power potential. Our data suggest that these size dependencies may also be present at higher densities further from the melting density. Simulations very close to melting suggest that the melting densities in the literature are incorrect.