{
  "abstract": "We study magnetic systems featuring competing antiferromagnetic and spin-nematic phases, described by dipolar primary and quadrupolar secondary order parameters. While the antiferromagnetic phase breaks time-reversal and spin-rotational symmetries, only spin-rotational symmetry is broken in the nematic phase, which can be understood as a spin-vestigial phase. We develop a classical continuum field theory with independent vector and tensor fields and use mean-field and renormalization group methods to analyze its phases and finite-temperature transitions. We determine the fixed-point structure using an $ε$ expansion about the upper critical dimension of six and track the resulting fixed points to lower dimensions using a perturbative fixed-dimension renormalization group approach. The multicritical fixed point governing the meeting of the antiferromagnetic, nematic, and paramagnetic phases occurs at imaginary coupling throughout the dimensions accessible to our analysis, indicating a first-order transition through the triple point. Away from the triple point, a direct paramagnetic-to-antiferromagnetic transition can be continuous when the tensor mass is sufficiently large, without an intervening vestigial phase. We argue that it is governed by the cubic universality class in $d=3$ and the Ising universality class in $d=2$ for three-component order parameters. The theory also supports a two-step transition with an intermediate spin-nematic phase. The paramagnetic-to-nematic transition is governed by the four-state Potts universality class in $d=2$ and is first order in $d=3$, while the nematic-to-antiferromagnetic transition is generically expected to be continuous and of Ising type in both dimensions. Our results provide a field-theoretical framework for understanding the finite-temperature transitions observed in the candidate Kitaev material Na$_2$Co$_2$TeO$_6$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28620",
  "author_total": 2,
  "authors": [
    {
      "name": "Niccolò Francini"
    },
    {
      "name": "Lukas Janssen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9rbne0y2p9fj2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28620",
  "fulltext_url": null,
  "id": "9rbne0y2p9fj2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28620",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.28620",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9rbne0y2p9fj2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.28620",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28620"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Competing magnetic and spin vestigial orders from continuum field theory",
  "title_text": "Competing magnetic and spin vestigial orders from continuum field theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/9rbne0y2p9fj2",
  "venue": "arXiv",
  "versions": []
}