Fisher Curvature Scaling at Critical Points: An Exact Information-Geometric Exponent

Key Points

• To introduce a new scaling exponent for scalar curvature on Fisher manifolds at critical points.
• Derived a scaling exponent d_R based on scalar curvature and critical parameters.
• Validated the exponent for 2D Ising models with high precision.
• Extended predictions to 3D Ising and Potts models (q=3 and q=4) and confirmed numerically.
• Achieved confirmation of d_R = 10/9 for the 2D Ising model to 4 significant figures.
• Numerical validations for the 3D Ising and Potts models support the extended predictions.