Correlation Function Decay
Correlation length ξ
5.0
Power-law exponent η
1.0
Oscillation frequency ω
0.0
Temperature proxy T
1.0
— exp decay
— power-law
— Ornstein-Zernike
Exponential: C(r) = e^(−r/ξ)
Power-law: C(r) = r^(−η)
Ornstein-Zernike:
C(r) ~ e^(−r/ξ) / r^((d−1)/2)
At T_c: ξ→∞, power-law
T≠T_c: exponential decay
Critical phenomena · universality · Ising model · T_c: ξ diverges → scale-free correlations