Determination of the algebraic exponents near the melting transition of a two-dimensional Lennard-Jones system

We report a calculation of algebraic exponents for translational order as well as for orientational order in a two-dimensional molecular-dynamics system containing 12 480 Lennard-Jones particles, near the melting transition. Results of the calculation, which proceeds via finite-size scaling, show that values of algebraic exponents are in better agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory than was hitherto assumed. Higher moments of the orientational order parameter, however, produce exponents deviating from those obtained with the zeroth moment. This observation of imperfect scaling is an illustration of the discriminative ability of the finite-size scaling approach, in the identification of algebraically ordered phases in molecular-dynamics simulations of large systems.