{
  "model": "TFIsing",
  "lattice": "square",
  "n_sites": "inf",
  "boundary": "TDL",
  "params": {
    "h": 3.04438
  },
  "instance_id": "TFIsing/square_inf_3.04438",
  "rows": [
    {
      "energy": -3.2342623,
      "sigma": null,
      "method": "iPEPS",
      "method_detail": "fit to D = 2, 3",
      "method_as_published": "iPEPS, finite correlation length extrapolation e(xi) = e(∞) - alpha*v*xi^3 (Eq. 17) fitted to the best D = 2 and D = 3 critical energies, using literature v = 3.323(33)",
      "bound_type": "extrapolated",
      "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)",
      "how_tdl": "extrapolation in the ansatz",
      "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566",
      "peer_reviewed": true,
      "source": "tdl-2026-10-25",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-25",
        "method": "arXiv:1803.08566: journal version: Phys. Rev. X 8, 031030 (2018), open-access PDF from journals.aps.org (journal/rader-prx.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 1803.08566v1 (only version on arXiv; PRX text not downloadable: APS blocks scripted access))); single reading, journal check, second reading 2026-10-25",
        "reported_as": "e(∞) ≈ −3.2342623",
        "note": "Eq. (18), Sec. III.B.4; line 578 of rader.plain.txt (sources/rader.plain.txt) | per site (energy density e = E/N_sites, stated near Eq. 16; Table B.1 header says only 'Energy /J'); units J; Eq. (15): H_TFI = -J sum_<i,j> sigma^z_i sigma^z_j - h sum_i sigma^x_i - h_z sum_i sigma^z_i (sigma as printed; the paper does not write 'Pauli', but h_c = 3.04438 is the Pauli-normalised critical field; J = 1 ferromagnetic, <i,j> nearest-neighbour bonds on infinite square lattice) | Printed with '≈' and no uncertainty; the paper itself says it is a conjecture ('If correct ... accurate to about 1e-6 already at D = 3') and relies on only two D values. The text gives alpha_iPEPS ≈ -0.00061.",
        "secondary_of": null
      }
    },
    {
      "energy": -3.233573421,
      "sigma": null,
      "method": "iPEPS",
      "method_detail": "D = 2",
      "method_as_published": "Best variational iPEPS energy (Table B.1 'Best variational energies')",
      "bound_type": "variational",
      "bound_type_reason": "variational state of the infinite system at a fixed ansatz size; energy per site is an upper bound up to the stated contraction (RULES.md 14.4)",
      "how_tdl": "infinite system",
      "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566",
      "peer_reviewed": true,
      "source": "tdl-2026-10-25",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-25",
        "method": "arXiv:1803.08566: journal version: Phys. Rev. X 8, 031030 (2018), open-access PDF from journals.aps.org (journal/rader-prx.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 1803.08566v1 (only version on arXiv; PRX text not downloadable: APS blocks scripted access))); single reading, journal check, second reading 2026-10-25",
        "reported_as": "−3.233 573 421",
        "note": "Table B.1 (TFI @hc block); line 1257 of rader.plain.txt (sources/rader.plain.txt) | per site (energy density e = E/N_sites, stated near Eq. 16; Table B.1 header says only 'Energy /J'); units J; Eq. (15): H_TFI = -J sum_<i,j> sigma^z_i sigma^z_j - h sum_i sigma^x_i - h_z sum_i sigma^z_i (sigma as printed; the paper does not write 'Pauli', but h_c = 3.04438 is the Pauli-normalised critical field; J = 1 ferromagnetic, <i,j> nearest-neighbour bonds on infinite square lattice) | Digits grouped in threes as printed. Row labelled 'TFI @hc' (critical point h = h_c, h_z = 0). Cross-checked against the layout extraction (same digits).",
        "secondary_of": null
      }
    },
    {
      "energy": -3.234260711,
      "sigma": null,
      "method": "iPEPS",
      "method_detail": "D = 3",
      "method_as_published": "Best variational iPEPS energy (Table B.1 'Best variational energies')",
      "bound_type": "variational",
      "bound_type_reason": "variational state of the infinite system at a fixed ansatz size; energy per site is an upper bound up to the stated contraction (RULES.md 14.4)",
      "how_tdl": "infinite system",
      "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566",
      "peer_reviewed": true,
      "source": "tdl-2026-10-25",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-25",
        "method": "arXiv:1803.08566: journal version: Phys. Rev. X 8, 031030 (2018), open-access PDF from journals.aps.org (journal/rader-prx.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 1803.08566v1 (only version on arXiv; PRX text not downloadable: APS blocks scripted access))); single reading, journal check, second reading 2026-10-25",
        "reported_as": "−3.234 260 711",
        "note": "Table B.1 (TFI @hc block); line 1258 of rader.plain.txt (sources/rader.plain.txt) | per site (energy density e = E/N_sites, stated near Eq. 16; Table B.1 header says only 'Energy /J'); units J; Eq. (15): H_TFI = -J sum_<i,j> sigma^z_i sigma^z_j - h sum_i sigma^x_i - h_z sum_i sigma^z_i (sigma as printed; the paper does not write 'Pauli', but h_c = 3.04438 is the Pauli-normalised critical field; J = 1 ferromagnetic, <i,j> nearest-neighbour bonds on infinite square lattice) | Digits grouped in threes as printed. Row labelled 'TFI @hc' (critical point h = h_c, h_z = 0). Cross-checked against the layout extraction (same digits).",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/instances/#x-TFIsing_square_inf_3_04438",
  "per_site_divisor": 1,
  "per_site_label": "E/N (Pauli)",
  "best": {
    "exact": null,
    "variational": {
      "energy": -3.234260711,
      "sigma": null,
      "method": "iPEPS",
      "ansatz": null,
      "method_detail": "D = 3",
      "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566",
      "bound_type": "variational",
      "energy_per_site": -3.234260711
    },
    "projected": null,
    "extrapolated": {
      "energy": -3.2342623,
      "sigma": null,
      "method": "iPEPS",
      "ansatz": null,
      "method_detail": "fit to D = 2, 3",
      "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566",
      "bound_type": "extrapolated",
      "energy_per_site": -3.2342623
    },
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -3.2342623,
    "sigma": null,
    "method": "iPEPS",
    "ansatz": null,
    "method_detail": "fit to D = 2, 3",
    "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566",
    "bound_type": "extrapolated",
    "energy_per_site": -3.2342623
  },
  "no_record_reason": null
}