{
  "abstract": "We employ pseudospectral methods to solve the homogeneous Ornstein-Zernike (OZ) equation for a model fluid in the vicinity of the critical point. Focusing on the Mean-Spherical Approximation (MSA) as a closure to the OZ equation, we obtain numerical estimates for the critical exponents $η$, $δ$ and $γ$ for a system of hard-core Yukawa particles both in two and three dimensions. The three-dimensional MSA exponents are already well-known from an analytic solution and are recovered by our numerical methods. The two-dimensional exponents are a new output of this work. The pseudospectral method allows for rapid and highly accurate solution of liquid-state integral equation theories, and enables calculations on truely infinite domains, as needed for highly correlated states. In addition, we analyse the standard Picard iteration scheme and propose a variation of it which provides increased stability and speed of convergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03627",
  "author_total": 4,
  "authors": [
    {
      "name": "Jake Skelton"
    },
    {
      "name": "Joseph Brader"
    },
    {
      "name": "Salomée Tschopp"
    },
    {
      "name": "Benjamin Goddard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2rv3vw31ys6x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03627",
  "fulltext_url": null,
  "id": "f2rv3vw31ys6x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03627",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.soft"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7208706445",
  "pdf_url": "https://arxiv.org/pdf/2609.03627",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f2rv3vw31ys6x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2609.03627",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03627"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Pseudospectral Methods and Critical Phenomena",
  "title_text": "Pseudospectral Methods and Critical Phenomena",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:31Z",
  "url": "https://research.draconitic.com/paper/f2rv3vw31ys6x",
  "venue": "arXiv",
  "versions": []
}