KPZ INTERFACE GROWTH

Kardar-Parisi-Zhang · Roughness β=1/3 · Family-Vicsek scaling
W(t) = —
β_eff = —
t = 0
∂h/∂t = ν∇²h + λ/2(∇h)² + η
KPZ (1986): universal roughening with β=1/3, α=1/2, z=3/2 in 1+1D.

Edwards-Wilkinson (λ=0): β=1/4.

Roughness W(t) = √⟨(h-h̄)²⟩ grows as t^β until saturation at L^α.

Top: Interface profile h(x,t) over time
Bottom: log W vs log t with β slope