Probabilistic characterization of the Widom delta in supercritical region

We present a probabilistic classification algorithm to understand the structural transition of supercritical Lennard-Jones (LJ) fluid. The classification algorithm is designed based on the exploratory data analysis on the nearest Voronoi neighbors of subcritical vapor and liquid. The algorithm is tested and applied to LJ type fluids modeled with the truncated and shifted potential and the Weeks-Chandler-Andersen potential. The algorithm makes it available to locate the Widom delta, which encloses the supercritical gas-liquid boundary and the percolation transition loci in a geometrical manner, and to conjecture the role of attractive interactions on the structural transition of supercritical fluids. Thus, the designed algorithm offers an efficient and comprehensible method to understand the phase behavior of a supercritical mesophase.