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