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).