100
10
20
N = –
R_g = –
End-to-end = –
Pivots accepted: –
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.
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.