Radial Distribution Function in a Two Dimensional Core-Shoulder Particle System

[2603.24537] Radial Distribution Function in a Two Dimensional Core-Shoulder Particle System Skip to main content Search Submit Donate Log in Condensed Matter > Soft Condensed Matter arXiv:2603.24537 (cond-mat) [Submitted on 25 Mar 2026 ( v1 ), last revised 14 Jul 2026 (this version, v3)] Title: Radial Distribution Function in a Two Dimensional Core-Shoulder Particle System Authors: Michael Wassermair , Gerhard Kahl , Andrew J Archer , Roland Roth View PDF HTML (experimental) Abstract: An important quantity in liquid state theory is the radial distribution function $g(r)$. It can be calculated within the framework of classical density functional theory in two very distinct ways. In the test-particle route, one fixes a single fluid particle, turning it into an external potential in which the inhomogeneous structure of the fluid is calculated by minimising the functional. The second route to $g(r)$ in density functional theory employs the Ornstein-Zernike equation and the pair direct correlation function, that can be obtained from the second functional derivatives of the excess (over the ideal gas) free energy functional. Since typically an approximate excess free energy functional is employed, the test-particle route, which requires only one functional derivative, is more accurate than the Ornstein-Zernike route. Here we study a two dimensional core-shoulder particle system and find that in some circumstances the results from the Ornstein-Zernike route can be comparable in accuracy to the test-particle results for $r>\sigma$, the core diameter. We also examine in detail the asymptotic $r\to\infty$ decay of $g(r)$, finding a variety of possible decay wavelengths at different state points and state points where there is a crossover from one wavelength to a very different one. This behaviour is a signature pointing to the rich phase behaviour of the incipient solid phases. Comments: 30 pages, 6 figures. A substantially different manuscript to the first arXiv upload version Subjects: Soft Condensed Matter (cond-mat.soft) ; Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2603.24537 [cond-mat.soft] (or arXiv:2603.24537v3 [cond-mat.soft] for this version) https://doi.org/10.48550/arXiv.2603.24537 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Phys. Chem. B 130, 8514 (2026) Related DOI : https://doi.org/10.1021/acs.jpcb.6c00653 Focus to learn more DOI(s) linking to related resources Submission history From: Andrew Archer [ view email ] [v1] Wed, 25 Mar 2026 17:12:46 UTC (175 KB) [v2] Tue, 7 Apr 2026 16:31:25 UTC (1 KB) (withdrawn) [v3] Tue, 14 Jul 2026 10:08:06 UTC (2,133 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.soft < prev | next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.stat-mech References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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