KPZ Interface Roughening

Kardar-Parisi-Zhang universality class — nonlinear stochastic growth with exact exponents χ=1/2, β=1/3, z=3/2

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Width W(t)

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β exponent (fit)

Time steps

Noise strength λ_noise 1.00

Nonlinearity λ (KPZ term) 1.00

Diffusion ν 0.50

Interface color 260°

The KPZ equation ∂h/∂t = ν∇²h + (λ/2)(∇h)² + η describes interface growth. The nonlinear term breaks up-down symmetry and places the system in the KPZ universality class with exact exponents β=1/3, χ=1/2, z=3/2 in 1+1D.