Zhuravlev/fisher-curvature-scaling

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:

$$d_R = \frac{d\nu + 2\eta}{d\nu + \eta}$$

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

Universality Classes

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}
}