Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids

In our previous work [Phys. Rev. E 104, 014124 (2021)2470-004510.1103/PhysRevE.104.014124], we developed a method for analyzing classical liquids using the functional renormalization group (FRG) without relying on a hard-core reference system. In this paper, we extend this method to three-dimensional liquids. We describe an efficient approach for performing the spatial integrals that appear in the renormalization group equations, which is essential for realizing numerical calculations in three dimensions. As a demonstration, we present its application to the Lennard-Jones liquids. Through calculations of thermodynamic quantities, we find that FRG preserves thermodynamic consistency (TC) better than traditional integral-equation methods such as the hypernetted-chain, Percus-Yevick, and Kovalenko-Hirata closures. Taking the molecular dynamics results as a benchmark, we also show that FRG can achieve an accuracy comparable to that of integral-equation methods that incorporate TC, such as the Rogers-Young closure. We further assess the accuracy of the pair distribution function and examine whether our method remains applicable below the critical temperature. Our results demonstrate that FRG provides a new method for describing classical liquids with accuracy comparable to modern liquid theories.