Fisher Curvature Scaling at Statistical Critical Points: A New Information-Geometric Exponent
Key Points
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.
Abstract
Proposes a new critical exponent dR for Fisher curvature scaling and conjectures dR = (d*nu + 2*eta) / (d*nu + eta). Validated on 2D Ising (exact TM L=3-9, MCMC L=10-20) and 3D Ising.