Eden Growth — KMC Surface Roughness

The Eden model (1961) grows clusters by adding cells to the perimeter with equal probability — a kinetic Monte Carlo process. The roughening exponent β≈1/3 and KPZ universality class describe the scaling of interface width W ~ t^β.

Model

Steps: 0 | Width W: — | β ≈ 1/3 (KPZ)

W²(t) = ⟨[h(x,t)−⟨h⟩]²⟩ | KPZ scaling: W ~ L^α f(t/L^z), β=1/3, α=1/2, z=3/2