{
  "model": "TFIsing",
  "lattice": "chain",
  "n_sites": 10,
  "boundary": "P",
  "params": {
    "h": 1
  },
  "instance_id": "TFIsing/chain_10_P_1",
  "rows": [
    {
      "energy": -12.784906442999322,
      "sigma": null,
      "energy_variance": null,
      "dof": 10,
      "einf": 0,
      "v_score": null,
      "method": "Exact Solution",
      "bound_type": "exact",
      "bound_type_reason": "exact diagonalization|ex",
      "reference": "[code](https://github.com/varbench/methods/blob/main/programs/exact_ising_1d/exact_ising_1d.py)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -12.784906442999326,
      "sigma": null,
      "energy_variance": 1.1e-13,
      "dof": 10,
      "einf": 0,
      "v_score": 6.729729009416381e-15,
      "method": "DMRG (bond dimension = 28)",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/TFIsing/chain_10_P_1/dmrg.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -12.785231,
      "sigma": 0.000048,
      "energy_variance": 0.0024565159,
      "dof": 10,
      "einf": 0,
      "v_score": 0.00015028042728314244,
      "method": "RBM (alpha = 1)",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/TFIsing/chain_10_P_1/vmc_rbm.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true,
      "defect": {
        "flag": "below-exact",
        "finding": "6.8 sigma below the exact ground state, which no variational state can be. Settled by rerun on 2026-09-11 (checks/results-tfising-rbm.json).",
        "diagnosis": "The published value is a minimum of the optimization trace, not a converged measurement. Three seeds each, netket 3.22.4, alpha=1 complex RBM, 2000 SR steps. Evaluating the trained parameters by FULL SUMMATION over all 1024 basis states (zero Monte-Carlo error) puts every converged energy ABOVE the exact value, as the variational principle requires, while every training trace dips 1.5e-3 to 3.5e-3 BELOW it. Each published value lies between the two.",
        "ruled_out": "Not an autocorrelation-underestimated error bar: tau_corr <= 0.05 and R_hat = 1.0000 across all six runs.",
        "evidence": "checks/results-tfising-rbm.json, checks/tfising_rbm_check.py"
      }
    },
    {
      "energy": -12.77246,
      "sigma": 0.0003,
      "energy_variance": 0.09330111,
      "dof": 10,
      "einf": 0,
      "v_score": 0.005719231921420692,
      "method": "Jastrow baseline",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/TFIsing/chain_10_P_1/vmc_jastrow.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    }
  ],
  "url": "https://qmbl.org/i/TFIsing/chain_10_P_1/",
  "per_site_divisor": 10,
  "per_site_label": "E/N (Pauli)",
  "record": {
    "energy": -12.784906442999326,
    "sigma": null,
    "method": "DMRG (bond dimension = 28)",
    "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/TFIsing/chain_10_P_1/dmrg.sh)",
    "energy_per_site": -1.2784906442999326
  },
  "no_record_reason": null
}