Finite-size scaling and interaction-range renormalization of critical phenomena in a three-dimensional Lennard–Jones fluid

Abstract

Finite-size effects and interaction-range truncation remain major challenges in accurately determining critical properties from Molecular Dynamics simulations of fluids. Here, the critical behavior of a three-dimensional Lennard–Jones fluid was investigated using Molecular Dynamics simulations combined with finite-size scaling, Binder cumulants, correlation-length analysis, and dynamic criticality measurements. Simulations were performed for system sizes ranging from  and cutoff radii from . As the vapor–liquid critical region was approached, the local-density susceptibility increased by more than a factor of three, while the correlation length grew from approximately () to over (), indicating the emergence of long-range density fluctuations. Finite-size extrapolation yielded thermodynamic-limit critical parameters of  and , in close agreement with established Lennard–Jones reference values. Dynamic analyses revealed pronounced critical slowing down, with relaxation times increasing by nearly an order of magnitude near criticality. Increasing the cutoff radius systematically shifted the critical temperature upward by approximately  and enhanced susceptibility amplitudes. A near-linear relationship was observed between the critical-temperature shift and the omitted tail energy, leading to the development of a unified energetic scaling framework based on the cumulative attraction parameter . The resulting universal renormalization curve establishes a direct microscopic-to-macroscopic connection between interaction truncation, fluctuation growth, and emergent critical behavior in finite molecular systems.