{
  "abstract": "When the Boltzmann weight is nonnegative, the actions of a lattice field theory define a family of probability distributions that forms a statistical manifold, and its Fisher metric gives the number of measurements needed to distinguish two nearby actions. In the large-$N$ limit of the two-dimensional lattice Gross-Neveu model with Wilson fermions, we study the continuum limit, in which the lattice spacing $a$ is taken to zero with the mass gap $Λ$ fixed, through the Fisher metric of the distribution of the auxiliary field $σ$. The renormalization condition fixes an expectation coordinate, and dimensional transmutation becomes an exponential relation between it and a natural coordinate. The main result is that the $a\\to0$ limits differ between the Fisher metric of the long-distance modes, whose momenta are fixed in physical units, and the Fisher metric of the full $P(σ)$. In the former, the lengths of the infinitely many irrelevant directions that change the kinetic term shrink, relative to the mass-term direction, to order $aΛ\\log(1/(aΛ))$ or smaller, and when several modes are combined, only the two directions $(Λ,m)$ of the continuum theory remain. In the latter, the kinetic-term directions shrink at the same rate as the mass-term direction, and the difference in the regularization remains in correlations at distances of the order of the lattice spacing. An exception is the deformation that only adds a contact term to the propagator: as $a\\to0$ its length goes to zero in both metrics, and it becomes indistinguishable from a change of the coupling $1/g^2$ (a lattice version of Kutasov's result). The curvature of the coupling plane at fixed kinetic term diverges as $(1/2)\\log^2(1/(aΛ))$, not as the correlation volume often assumed in thermodynamic geometry, and the critical point is infinitely far in Fisher distance from any point at finite $a$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34277",
  "author_total": 1,
  "authors": [
    {
      "name": "Akio Tomiya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eenst3rxse74n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34277",
  "fulltext_url": null,
  "id": "eenst3rxse74n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34277",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "hep-lat"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7223897840",
  "pdf_url": "https://arxiv.org/pdf/2610.34277",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eenst3rxse74n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.34277",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34277"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Information geometry of continuum limits in lattice field theory: The Gross-Neveu model with Wilson fermions",
  "title_text": "Information geometry of continuum limits in lattice field theory: The Gross-Neveu model with Wilson fermions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/eenst3rxse74n",
  "venue": "arXiv",
  "versions": []
}