What question did this study set out to answer?

To explore the scaling behavior of scalar curvature in alpha-power Fisher metrics at the 2D Ising critical point.

March 3, 2026Open Access

A Linear Exponent Law for Alpha-Power Fisher Curvature at the 2D Ising Critical Point

Key Points

To explore the scaling behavior of scalar curvature in alpha-power Fisher metrics at the 2D Ising critical point.
Utilized exact enumeration for system sizes L=3,4,5.
Analyzed the scaling relationship of scalar curvature.
Derived the linear law for curvature scaling with respect to alpha.
Scalar curvature scales as R ~ n^{d_R(alpha)}.
Identified d_R converging to a linear law as d_R(alpha) = alpha * d_R(1).
Showed a consistent relationship between curvature and alpha for the Ising model.

Abstract

Exact enumeration (L=3, 4, 5) reveals that scalar curvature of alpha-power Fisher metrics scales as R ~ n^dR (alpha) with dR converging to the linear law dR (alpha) = alpha * dR (1).

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Cite This Study

Max Zhuravlev (Sun,) studied this question.

synapsesocial.com/papers/69a67efaf353c071a6f0abff https://doi.org/https://doi.org/10.5281/zenodo.18827254