Self-avoiding walks (SAW) as polymer models. Compare SAW (ν≈0.588 in 3D, ν=3/4 in 2D) with simple random walk (ν=1/2). Watch end-to-end distance scaling R~N^ν.
Self-avoiding walks model polymer chains in good solvents. Flory theory: ν=3/(d+2) → ν=3/4 in 2D, ν=3/5 in 3D. Exact 2D result: ν=3/4 (Nienhuis 1982 via Coulomb gas). Upper critical dimension d=4 where SAW→RW (ν=1/2). The number of SAWs of length N scales as μ^N · N^(γ-1) where μ is the lattice connective constant.