Ising Wolff Clusters

Cluster flip algorithm — large correlated clusters flip at Tc = 2/ln(1+√2) ≈ 2.269

Colored cluster = last flipped
Tc = 2.2691... ←
Wolff algorithm:
1. Pick random site i
2. Add same-spin neighbors
with prob p=1−e^(−2J/kT)
3. Flip entire cluster

At T_c: cluster size
~ N (system size!)
Critical slowing down
eliminated vs. Metropolis

χ = β(⟨M²⟩−⟨M⟩²)
peaks sharply at T_c
Computing...