{
  "abstract": "Physical decoherence can preserve the microscopic strategic neutrality (i.e. zero effective field and equal potential of the two homogeneous strategic orientations) of a quantum game while changing the thermodynamic regime of the corresponding interacting population. We demonstrate this for an Eisert--Wilkens--Lewenstein (\\textit{EWL}) Stag Hunt embedded as independent nearest neighbor encounters on a square lattice. For the restricted strategies $\\mathsf{Q}=i\\mathbb{Z}$ and $\\mathsf{D}=i\\mathbb{Y}$, noisy two-player payoff matrices are determined for phase damping, depolarization, and amplitude damping and mapped exactly to channel dependent Ising parameters $\\mathfrak{J}(Γ,p)$ and $\\mathfrak{H}(Γ,p)$. Phase damping and depolarization show the clearest contrast: they share the same microscopic neutrality branch $\\mathfrak{H}=0$, while only depolarization suppresses the interaction as $(1-p)^2$. At $β=1$, this produces an exact depolarization-driven square-lattice critical point at $p_{*}\\approx 0.233460\\ldots$, whereas phase damping remains in the ordered coexistence regime along the same neutrality branch. Monte Carlo finite size scaling is consistent with two-dimensional Ising criticality and distinguishes field driven coexistence below $p_{*}$ from a smooth crossover above it. Amplitude damping additionally reveals a strong dependence on channel placement: the post-strategy neutrality branch reaches $Γ=0$ at $p=1/3$ and then disappears. Resource negativity further shows that microscopic two-qubit entanglement and collective interaction strength are distinct quantities. The resulting extended lattice remains an ordinary classical Ising system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02957",
  "author_total": 1,
  "authors": [
    {
      "name": "Rajdeep Tah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6mzz7hj4fa2r0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02957",
  "fulltext_url": null,
  "id": "6mzz7hj4fa2r0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02957",
  "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"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7208742291",
  "pdf_url": "https://arxiv.org/pdf/2609.02957",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6mzz7hj4fa2r0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.02957",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02957"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt",
  "title_text": "Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/6mzz7hj4fa2r0",
  "venue": "arXiv",
  "versions": []
}