{
  "abstract": "Long-range interactions can protect dissipative order against fluctuations, but determining when they do so in two dimensions remains out of reach for existing many-body methods. We develop a continuous SU(2)-covariant truncated-Wigner framework that maps the problem onto stochastic dynamics with one Bloch sphere per site. Derived systematically from the exact Stratonovich-Weyl evolution of the Lindblad equation, it generates both drift and reservoir noise for arbitrary spin $S$. Benchmarks against exact and tensor-network calculations validate its description of non-equilibrium dynamics and steady states. Applied to 400-site two-dimensional dissipative anisotropic XY lattices, our method reveals physics missed by mean-field and perturbative approaches: vortex-antivortex proliferation destroys the predicted staggered-XY phase for nearest-neighbour coupling, whereas algebraically decaying interactions stabilize an extended $\\mathbb{Z}_2$-ordered phase. We obtain the first beyond-mean-field steady-state phase diagram of the long-range interacting model, revealing reentrant loss of order at strong coupling and closure of the ordered region beyond $α\\approx 3.5$. Our new method provides a scalable route to strongly correlated driven-dissipative systems with long-range interactions, higher-dimensional geometries, spin-boson couplings, and spins beyond one half, relevant to modern experiments with magnetic atoms and polar molecules in optical lattices and tweezer arrays.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27462",
  "author_total": 3,
  "authors": [
    {
      "name": "Igor Timofeev"
    },
    {
      "name": "Dawid A. Hryniuk"
    },
    {
      "name": "Marzena H. Szymańska"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/enezgtdj47ydf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27462",
  "fulltext_url": null,
  "id": "enezgtdj47ydf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27462",
  "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.quant-gas"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7223155503",
  "pdf_url": "https://arxiv.org/pdf/2610.27462",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/enezgtdj47ydf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27462",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27462"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "amo"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Systematic Truncated Wigner Approximation for Open Spin Systems Reveals Long-Range Order Far from Equilibrium",
  "title_text": "Systematic Truncated Wigner Approximation for Open Spin Systems Reveals Long-Range Order Far from Equilibrium",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/enezgtdj47ydf",
  "venue": "arXiv",
  "versions": []
}