{
  "abstract": "We introduce a new Euclidean quantum model with zero-spin scaled scalar fields on a spacetime hypercubic lattice, which we refer to as the hybrid model. The model coupling parameters are the hopping parameter $κ^2>0$ and the field interaction coupling $α>0$. Using the technique of lattice scaled fields, with a noncanonical scaling that corresponds to a partial renormalization (wave function renormalization), we show that the partition function of this model satisfies both thermodynamic and ultraviolet stability bounds, with constants which are uniform in the lattice volume $Λ_s$ and the lattice spacing $a\\in(0,1]$. As a consequence, the model has a finite free energy per degree of freedom in the thermodynamic limit $Λ_s\\nearrow\\infty$, at least in the subsequential sense. Subsequently, we can also take the ultraviolet or continuum limit $a\\searrow 0$. Besides the finiteness property of the free energy, for sufficiently small values of the model coupling parameters $κ^2$ and $α$, we show the model satisfies Osterwalder-Schrader positivity and construct the underlying physical quantum mechanical Hilbert space, and, using a polymer expansion, we show correlations also remain bounded in the thermodynamic limit. Finally, we perturbatively compute an infinite volume truncated four-point correlation showing it is nonzero. Noting that, for fixed $a$, perturbation series in $κ^2$ and $α$ converges, these results are sufficient to show that our hybrid model makes sense as a lattice quantum field theory in spacetime dimension $d=3,4$, with possible extensions to other higher values of $d$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19310",
  "author_total": 3,
  "authors": [
    {
      "name": "P. A. Faria da Veiga"
    },
    {
      "name": "R. Mistry"
    },
    {
      "name": "M. O'Carroll"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/947a3ny3912pw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19310",
  "fulltext_url": null,
  "id": "947a3ny3912pw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19310",
  "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",
      "hep-lat"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|advanced mathematical theories"
    ]
  ],
  "openalex": "W7222287688",
  "pdf_url": "https://arxiv.org/pdf/2610.19310",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/947a3ny3912pw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.19310",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19310"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "A Nontrivial Lattice Scalar Quantum Field Model",
  "title_text": "A Nontrivial Lattice Scalar Quantum Field Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/947a3ny3912pw",
  "venue": "arXiv",
  "versions": []
}