Local structure, fluctuations, and freezing in two dimensions

Starting from the concept of local solidlike order in two-dimensional (2D) liquids we introduce and quantify the corresponding ensembles of fluctuations, using a probabilistic-based method of local-structure analysis (LSA). A systematic LSA (including size dependence) was performed for a hard disk and 2D Lennard-Jones systems, simulated using Monte Carlo and molecular-dynamics methods. We find that the onset of freezing is accompanied by a dramatic crossover between ensembles of fluctuations. Some universal features related to the onset of freezing in two dimensions are found and corresponding freezing criteria are formulated: (i) the liquid starts to freeze when the concentration of solidlike atoms constitutes 0.50-0.56, and (ii) a Lindemann-like freezing criterion: the rms fluctuation constitutes, at the onset, 0.12-0.13. Those criteria offer an effective method for a localization of the onset of freezing in computer simulations. We point out, in this context, that in computer simulations there is a possibility that all quantitative characterizations of the onset of freezing are related to a metastable range. This important methodological topic is discussed briefly in the light of recent results both for 2D and 3D systems.