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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.16710 |
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| _version_ | 1866918380476301312 |
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| author | Yokota, Takeru Haruyama, Jun Sugino, Osamu |
| author_facet | Yokota, Takeru Haruyama, Jun Sugino, Osamu |
| contents | In our previous work [Phys. Rev. E 104, 014124 (2021)], 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16710 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids Yokota, Takeru Haruyama, Jun Sugino, Osamu Soft Condensed Matter Statistical Mechanics High Energy Physics - Theory In our previous work [Phys. Rev. E 104, 014124 (2021)], 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. |
| title | Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids |
| topic | Soft Condensed Matter Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.16710 |