Scaling Hypothesis

Widom scaling: thermodynamic functions collapse onto universal curves near Tc

Exponents

Widom Scaling

f(t,h) = |t|^(2-α) F(h/|t|^(βδ))
M(t,h) = |t|^β G(h/|t|^(βδ))
Scaling collapse: different isotherms fall on a single curve when axes are rescaled by powers of |t|.
γ = β(δ−1)
α + 2β + γ = 2 (Rushbrooke)
Ising 3D exponents (shown): β≈0.326, δ≈4.8, γ≈1.237. Mean field: β=1/2, δ=3, γ=1.