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This work presents a new critical exponent related to Fisher curvature scaling in statistical systems.

March 3, 2026Open Access

Fisher Curvature Scaling at Statistical Critical Points: A New Information-Geometric Exponent

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This work presents a new critical exponent related to Fisher curvature scaling in statistical systems.
Proposed the critical exponent d_R for Fisher curvature scaling.
Validated the conjectured relationship using 2D Ising model with exact transfer matrix on sizes L=3-9 and MCMC on sizes L=10-20.
Applied investigation to the 3D Ising model.
Validated the conjecture d_R = (d*nu + 2*eta)/(d*nu + eta).
Demonstrated consistency across different sizes of the Ising models.

Implication

Proposes a new critical exponent for Fisher curvature scaling, indicating insights into Ising models.

Abstract

Proposes a new critical exponent d_R for Fisher curvature scaling and conjectures d_R = (d*nu + 2*eta)/(d*nu + eta). Validated on 2D Ising (exact TM L=3-9, MCMC L=10-20) and 3D Ising.

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Cite This Study

Max Zhuravlev (2026) studied this question.

synapsesocial.com/papers/69a67eebf353c071a6f0aa04 https://doi.org/10.5281/zenodo.18827215

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Implication

Proposes a new critical exponent for Fisher curvature scaling, indicating insights into Ising models.

Abstract

Proposes a new critical exponent d_R for Fisher curvature scaling and conjectures d_R = (d*nu + 2*eta)/(d*nu + eta). Validated on 2D Ising (exact TM L=3-9, MCMC L=10-20) and 3D Ising.

Fisher Curvature Scaling at Statistical Critical Points: A New Information-Geometric Exponent

Key Points

Implication

Abstract

Discussion

Cite This Study

Fisher Curvature Scaling at Statistical Critical Points: A New Information-Geometric Exponent

Key Points

Implication

Abstract

Discussion

Cite This Study

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