Entropy, correlations, and ordering in two dimensions

The ordering of simple fluids in two dimensions was investigated using the residual multiparticle entropy (RMPE) as a measure of the relevance of corr elations involving more than two particles in the configurational entropy o f the system. To this end, we performed Monte Carlo simulations of two prot otype systems, i.e., Lennard-Jones particles and hard discs. Consistent wit h previous studies, we found that, on approaching the freezing transition, the RMPE of the fluid undergoes a change from negative to positive values. However, in two dimensions the vanishing of the RMPE appears to be more dir ectly related to the formation of six-fold orientationally ordered patches, a process which foreshadows the freezing transition. The specificity of th e structural condition attained by the fluid in a state corresponding to a vanishing RMPE was further corroborated by an analysis of the shape of the radial distribution function (RDF): in fact, it turns out that the spatial profiles of the RDF of the Lennard-Jones fluid along a zero-RMPE locus can be superimposed at medium and large distances notwithstanding the differenc e of density and/or temperature of the corresponding thermodynamic states. The same long-range profile of the RDF is shared also by hard discs in the cited condition. Such a "scaling" property also holds in three dimensions w here it provides a suggestive nexus between the ordering criterion based on the vanishing of the RMPE and the Hansen-Verlet freezing rule. (C) 2000 Am erican Institute of Physics. [S0021-9606(00)51331-2].