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