{
  "abstract": "We present a one-dimensional classical statistical physics model on an infinite lattice with nearest-neighbor interactions and local state space $\\mathbb{Z}^2$, with a ``helical\" symmetry group $\\mathbb{Z}^2\\rtimes \\mathbb{Z}$ mixing flavor symmetry with spatial translation. For any $0<β<\\infty$, we construct an uncountable infinity of DLR (Gibbs) states parameterized by $\\mathbb{R}^2$, with a free $\\mathbb{Z}^2$ flavor symmetry group action; as such, we interpret the model as exhibiting spontaneous symmetry breaking at any temperature. The most general DLR state we construct is interpreted as an infinite sequence of localized domain walls separating a pair of asymptotic ``symmetry sectors\". Although any normalizable Gibbs state necessarily breaks a countably infinite freely-acting symmetry group, a natural regularization of the problem to (arbitrarily) large but finite systems with periodic boundary conditions has measure concentration in disjoint and far-separated symmetry-related clusters in the (now unique) Gibbs state, which justifies our interpretation of spontaneous symmetry breaking on the infinite line. A modification of the model with local state space $\\mathbb{R}^2$ must break a continuous helical symmetry at any temperature. This is not a contradiction with the Mermin-Wagner Theorem, because this continuous helical symmetry is non-compact and does not commute with translation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07693",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrew Lucas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fxg3xfcvprhvm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07693",
  "fulltext_url": null,
  "id": "fxg3xfcvprhvm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07693",
  "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.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7220999265",
  "pdf_url": "https://arxiv.org/pdf/2610.07693",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fxg3xfcvprhvm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.07693",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07693"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Spontaneous symmetry breaking at any temperature in a local one-dimensional model",
  "title_text": "Spontaneous symmetry breaking at any temperature in a local one-dimensional model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/fxg3xfcvprhvm",
  "venue": "arXiv",
  "versions": []
}