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Zhuravlev
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fisher-curvature-scaling

Tasks:
Tabular Regression
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n<1K
ArXiv:
Tags:
physics
statistical-mechanics
information-geometry
critical-phenomena
Fisher-information
curvature
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The dataset viewer is not available for this subset.
Cannot get the split names for the config 'default' of the dataset.
Exception:    SplitsNotFoundError
Message:      The split names could not be parsed from the dataset config.
Traceback:    Traceback (most recent call last):
                File "/usr/local/lib/python3.12/site-packages/datasets/inspect.py", line 286, in get_dataset_config_info
                  for split_generator in builder._split_generators(
                                         ^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 91, in _split_generators
                  pa_table = next(iter(self._generate_tables(**splits[0].gen_kwargs, allow_full_read=False)))[1]
                             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 193, in _generate_tables
                  examples = [ujson_loads(line) for line in batch.splitlines()]
                              ^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/utils/json.py", line 20, in ujson_loads
                  return pd.io.json.ujson_loads(*args, **kwargs)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
              ValueError: Expected object or value
              
              The above exception was the direct cause of the following exception:
              
              Traceback (most recent call last):
                File "/src/services/worker/src/worker/job_runners/config/split_names.py", line 65, in compute_split_names_from_streaming_response
                  for split in get_dataset_split_names(
                               ^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/inspect.py", line 340, in get_dataset_split_names
                  info = get_dataset_config_info(
                         ^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/inspect.py", line 291, in get_dataset_config_info
                  raise SplitsNotFoundError("The split names could not be parsed from the dataset config.") from err
              datasets.inspect.SplitsNotFoundError: The split names could not be parsed from the dataset config.

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Fisher Curvature Scaling at Statistical Critical Points

Data accompanying arXiv:2603.07651 -- Fisher Curvature Scaling at Statistical Critical Points: A New Information-Geometric Exponent.

Dataset Description

Numerical measurements of the Fisher information scalar curvature |R| at criticality for 8 universality classes, supporting the Scaling Closure Theorem:

dR=dν+2ηdν+ηd_R = \frac{d\nu + 2\eta}{d\nu + \eta}

where d_R is the curvature scaling exponent, d is spatial dimension, and (nu, eta) are standard critical exponents.

Universality Classes

Model d nu eta d_R (predicted) Sizes
2D Ising 2 1 1/4 10/9 = 1.111 L=3-20
2D Potts q=3 2 5/6 4/15 33/29 = 1.138 L=3-38
2D Potts q=4 2 2/3 1/4 22/19 = 1.158 L=3-36
3D Ising 3 0.630 0.036 1.019 L=4-10
3D XY 3 0.672 0.038 1.019 L=4-10
3D Heisenberg 3 0.711 0.038 1.017 L=4-10
BKT (2D clock/XY) 2 inf 1/4 1.0 --
Gaussian (free field) any 1/2 0 1.0 --

Data Files

  • data/ising_2d.json -- 2D Ising model (TM L=3-9 exact + MCMC L=10-20)
  • data/potts_q3.json -- 2D Potts q=3 (TM L=3-6 + MCMC L=32-38)
  • data/potts_q4.json -- 2D Potts q=4 (TM L=3-5 + MCMC L=4-36)
  • data/ising_3d.json -- 3D Ising (Wolff MCMC L=4-10)
  • data/xy_3d.json -- 3D XY (Wolff MCMC L=4-10)
  • data/heisenberg_3d.json -- 3D Heisenberg (Wolff MCMC L=4-10)
  • data/bz_decomposition_ising2d.json -- Brillouin zone decomposition (2D Ising L=3-9)
  • data/scaling_closure_theorem.json -- Theorem parameters for all 8 classes
  • data/reference_R_vs_L.json -- Reference scaling data

Methods

  • Transfer Matrix (TM): Exact diagonalization of 2^L transfer matrix
  • MCMC: Wolff cluster algorithm with jackknife error estimation
  • BZ decomposition: Fourier decomposition of curvature into momentum shells

Replication

Full replication code: Vibecodium/fisher-curvature-replication

Citation 

@article{zhuravlev2026fisher,
  title={Fisher Curvature Scaling at Statistical Critical Points: A New Information-Geometric Exponent},
  author={Zhuravlev, Maxim},
  journal={arXiv preprint arXiv:2603.07651},
  year={2026}
}
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