{
  "format_version": 1,
  "model": "periodic transverse-field Ising ring, even-parity pair gap",
  "formula": "Delta_+/J = 4 sqrt(1 + gamma^2 - 2 gamma cos(pi/L))",
  "lengths": [
    4,
    6,
    8,
    10,
    12
  ],
  "reference_x": [
    -2.0,
    -1.0,
    0.0,
    1.0,
    2.0
  ],
  "records": [
    {
      "L": 4,
      "points": [
        {
          "reference_x": -2.0,
          "gamma": 0.5,
          "gap_over_J": 2.947251516415801,
          "L_gap_over_J": 11.789006065663203
        },
        {
          "reference_x": -1.0,
          "gamma": 0.75,
          "gap_over_J": 2.833626166508712,
          "L_gap_over_J": 11.334504666034848
        },
        {
          "reference_x": 0.0,
          "gamma": 1.0,
          "gap_over_J": 3.061467458920718,
          "L_gap_over_J": 12.245869835682871
        },
        {
          "reference_x": 1.0,
          "gamma": 1.25,
          "gap_over_J": 3.565912050589316,
          "L_gap_over_J": 14.263648202357263
        },
        {
          "reference_x": 2.0,
          "gamma": 1.5,
          "gap_over_J": 4.249573449541226,
          "L_gap_over_J": 16.998293798164905
        }
      ]
    },
    {
      "L": 6,
      "points": [
        {
          "reference_x": -2.0,
          "gamma": 0.6666666666666667,
          "gap_over_J": 2.1531146037875195,
          "L_gap_over_J": 12.918687622725116
        },
        {
          "reference_x": -1.0,
          "gamma": 0.8333333333333334,
          "gap_over_J": 2.0042705265323044,
          "L_gap_over_J": 12.025623159193827
        },
        {
          "reference_x": 0.0,
          "gamma": 1.0,
          "gap_over_J": 2.0705523608201655,
          "L_gap_over_J": 12.423314164920992
        },
        {
          "reference_x": 1.0,
          "gamma": 1.1666666666666667,
          "gap_over_J": 2.3337015025831263,
          "L_gap_over_J": 14.002209015498757
        },
        {
          "reference_x": 2.0,
          "gamma": 1.3333333333333333,
          "gap_over_J": 2.737522094213743,
          "L_gap_over_J": 16.425132565282457
        }
      ]
    },
    {
      "L": 8,
      "points": [
        {
          "reference_x": -2.0,
          "gamma": 0.75,
          "gap_over_J": 1.6813361412070817,
          "L_gap_over_J": 13.450689129656654
        },
        {
          "reference_x": -1.0,
          "gamma": 0.875,
          "gap_over_J": 1.5431698188093144,
          "L_gap_over_J": 12.345358550474515
        },
        {
          "reference_x": 0.0,
          "gamma": 1.0,
          "gap_over_J": 1.5607225761290264,
          "L_gap_over_J": 12.485780609032211
        },
        {
          "reference_x": 1.0,
          "gamma": 1.125,
          "gap_over_J": 1.7292590406280026,
          "L_gap_over_J": 13.834072325024021
        },
        {
          "reference_x": 2.0,
          "gamma": 1.25,
          "gap_over_J": 2.011173463316511,
          "L_gap_over_J": 16.089387706532086
        }
      ]
    },
    {
      "L": 10,
      "points": [
        {
          "reference_x": -2.0,
          "gamma": 0.8,
          "gap_over_J": 1.3758463514666421,
          "L_gap_over_J": 13.75846351466642
        },
        {
          "reference_x": -1.0,
          "gamma": 0.9,
          "gap_over_J": 1.2528257383609178,
          "L_gap_over_J": 12.528257383609178
        },
        {
          "reference_x": 0.0,
          "gamma": 1.0,
          "gap_over_J": 1.2514757203218474,
          "L_gap_over_J": 12.514757203218474
        },
        {
          "reference_x": 1.0,
          "gamma": 1.1,
          "gap_over_J": 1.3721554672888183,
          "L_gap_over_J": 13.721554672888184
        },
        {
          "reference_x": 2.0,
          "gamma": 1.2,
          "gap_over_J": 1.587271172253219,
          "L_gap_over_J": 15.87271172253219
        }
      ]
    },
    {
      "L": 12,
      "points": [
        {
          "reference_x": -2.0,
          "gamma": 0.8333333333333334,
          "gap_over_J": 1.1632235712604686,
          "L_gap_over_J": 13.958682855125623
        },
        {
          "reference_x": -1.0,
          "gamma": 0.9166666666666666,
          "gap_over_J": 1.0538596712237223,
          "L_gap_over_J": 12.646316054684668
        },
        {
          "reference_x": 0.0,
          "gamma": 1.0,
          "gap_over_J": 1.0442095377604124,
          "L_gap_over_J": 12.530514453124947
        },
        {
          "reference_x": 1.0,
          "gamma": 1.0833333333333333,
          "gap_over_J": 1.1368153469627644,
          "L_gap_over_J": 13.641784163553172
        },
        {
          "reference_x": 2.0,
          "gamma": 1.1666666666666667,
          "gap_over_J": 1.3101705727318735,
          "L_gap_over_J": 15.722046872782482
        }
      ]
    }
  ],
  "critical_log_fits": [
    {
      "minimum_L": 4,
      "included_L": [
        4,
        6,
        8,
        10,
        12
      ],
      "intercept": 2.4793665997008576,
      "amplitude": 11.933703212282428,
      "slope": -0.9793333330927163,
      "z_estimate": 0.9793333330927163
    },
    {
      "minimum_L": 6,
      "included_L": [
        6,
        8,
        10,
        12
      ],
      "intercept": 2.4978599340675456,
      "amplitude": 12.156450497709464,
      "slope": -0.9875499750111932,
      "z_estimate": 0.9875499750111932
    },
    {
      "minimum_L": 8,
      "included_L": [
        8,
        10,
        12
      ],
      "intercept": 2.5062333590112034,
      "amplitude": 12.258668985704887,
      "slope": -0.9911218420247615,
      "z_estimate": 0.9911218420247615
    }
  ],
  "exact_limit_residuals": [
    {
      "minimum_L": 4,
      "rms_to_exact_scaling_limit": 1.212135815686511
    },
    {
      "minimum_L": 6,
      "rms_to_exact_scaling_limit": 0.9476978236577933
    },
    {
      "minimum_L": 8,
      "rms_to_exact_scaling_limit": 0.8033122101894087
    }
  ],
  "collapse_metric": {
    "description": "ordinary least-squares quartic common curve in each candidate's rescaled coordinates; RMS is descriptive for exact data",
    "candidate_scores": [
      {
        "minimum_L": 4,
        "candidates": [
          {
            "name": "Ising",
            "gamma_c": 1.0,
            "nu": 1.0,
            "z": 1.0,
            "quartic_coefficients_low_to_high": [
              12.440047253195885,
              0.8905604174189636,
              0.6041921771715258,
              -0.032239560886527165,
              -0.009906611035554794
            ],
            "rms_common_curve_residual": 0.46709825312314157,
            "point_count": 25
          },
          {
            "name": "shifted-critical-point",
            "gamma_c": 0.98,
            "nu": 1.0,
            "z": 1.0,
            "quartic_coefficients_low_to_high": [
              12.182628171388838,
              0.5371012906718032,
              0.9551202224802081,
              0.039668546493460285,
              -0.09648555868924394
            ],
            "rms_common_curve_residual": 0.5208810073511863,
            "point_count": 25
          },
          {
            "name": "changed-exponents",
            "gamma_c": 1.0,
            "nu": 0.8,
            "z": 1.1,
            "quartic_coefficients_low_to_high": [
              15.243143390871293,
              0.8679992199343459,
              0.20098508715704794,
              -0.03326270439632012,
              0.004787900484928714
            ],
            "rms_common_curve_residual": 0.760351279050302,
            "point_count": 25
          }
        ]
      },
      {
        "minimum_L": 6,
        "candidates": [
          {
            "name": "Ising",
            "gamma_c": 1.0,
            "nu": 1.0,
            "z": 1.0,
            "quartic_coefficients_low_to_high": [
              12.488591607574131,
              0.733536760147089,
              0.6155834406315012,
              -0.026778631521844204,
              -0.011028132589828666
            ],
            "rms_common_curve_residual": 0.24437172227653675,
            "point_count": 20
          },
          {
            "name": "shifted-critical-point",
            "gamma_c": 0.98,
            "nu": 1.0,
            "z": 1.0,
            "quartic_coefficients_low_to_high": [
              12.312149073382646,
              0.42510991836493717,
              0.7803376564933622,
              0.01608654894900779,
              -0.0533172125926973
            ],
            "rms_common_curve_residual": 0.30006553074151576,
            "point_count": 20
          },
          {
            "name": "changed-exponents",
            "gamma_c": 1.0,
            "nu": 0.8,
            "z": 1.1,
            "quartic_coefficients_low_to_high": [
              15.541802144965969,
              0.6234378841827519,
              0.2162468690365016,
              -0.016705409649507803,
              0.001975236877839913
            ],
            "rms_common_curve_residual": 0.45297388434849245,
            "point_count": 20
          }
        ]
      },
      {
        "minimum_L": 8,
        "candidates": [
          {
            "name": "Ising",
            "gamma_c": 1.0,
            "nu": 1.0,
            "z": 1.0,
            "quartic_coefficients_low_to_high": [
              12.510350755125224,
              0.6362089605327241,
              0.6207491755718586,
              -0.023295765083221502,
              -0.01154273899146342
            ],
            "rms_common_curve_residual": 0.13287510802043087,
            "point_count": 15
          },
          {
            "name": "shifted-critical-point",
            "gamma_c": 0.98,
            "nu": 1.0,
            "z": 1.0,
            "quartic_coefficients_low_to_high": [
              12.378873247403284,
              0.3415263705349622,
              0.6871296688456933,
              0.00349367974639574,
              -0.030347403205555103
            ],
            "rms_common_curve_residual": 0.17839616187893761,
            "point_count": 15
          },
          {
            "name": "changed-exponents",
            "gamma_c": 1.0,
            "nu": 0.8,
            "z": 1.1,
            "quartic_coefficients_low_to_high": [
              15.749942566218369,
              0.48816036798898216,
              0.2264772756400601,
              -0.0090355594211717,
              0.00023119607542464228
            ],
            "rms_common_curve_residual": 0.2726045952099337,
            "point_count": 15
          }
        ]
      }
    ],
    "statistical_boundary": "No sampling noise is present, so these scores do not define a parameter covariance matrix or confidence interval."
  },
  "thermal_cases": [
    {
      "gamma": 0.9,
      "bulk_gap_over_J": 0.2,
      "kBT_over_J": 0.05,
      "J_tau_T_over_hbar": 20.0,
      "J_xi_tau_over_hbar": 5.0,
      "fermion_occupation": 0.01798620996209156,
      "fan_edge_gamma": [
        0.975,
        1.025
      ]
    },
    {
      "gamma": 0.9,
      "bulk_gap_over_J": 0.2,
      "kBT_over_J": 0.2,
      "J_tau_T_over_hbar": 5.0,
      "J_xi_tau_over_hbar": 5.0,
      "fermion_occupation": 0.2689414213699951,
      "fan_edge_gamma": [
        0.9,
        1.1
      ]
    }
  ]
}