Flory Polymer Scaling — Self-Avoiding Random Walk

Self-avoiding walks model polymer chains in good solvents. The Flory exponent ν≈0.75 in 2D means R~N^0.75, much larger than the random walk prediction ν=0.5.

End-to-end distance R
R = 0.00
Fitted Flory exponent
ν = —
Theory: SAW ν≈0.75, RW ν=0.50
Flory (1949) argued ν = (d+2)/(2d+4), giving ν=3/4 in d=2. This is exact! Proved rigorously for 2D by Nienhuis (1982) using Coulomb gas methods. The excluded volume interaction swells the chain far beyond Gaussian (random walk) statistics.

For d=3: ν≈0.588 (exact: 0.5877... from RG, not the Flory value 0.6).