Polymer Self-Avoiding Walks

Pivot algorithm on 2D square lattice — radius of gyration R_g ~ N^ν with ν≈0.75 (Flory exponent)
100
10
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N =
R_g =
End-to-end =
Pivots accepted:
Pivot Algorithm
Pick random monomer as pivot. Apply random lattice symmetry (rotation/reflection) to one arm. Accept if result is self-avoiding. Extremely efficient: O(N log N) per accepted move. Flory (1949): ν = 3/(d+2) → ν = 3/4 in 2D. Exact: ν = ¾ (Nienhuis 1982, using Coulomb gas). Random walk would give ν = ½.