Exact RG flow: K' = ½ ln cosh(2K) — no finite-T transition in 1D
K=0.80 → flows to K=0 (disordered)
1D Ising decimation: integrate out every other spin analytically.
Recursion: K' = ½ ln cosh(2K). Fixed points: K*=0 (disordered, stable) and K*=∞ (ordered, unstable).
Since K' < K for all finite K, ALL trajectories flow to K=0 — no phase transition at finite T.
This reflects the exact result: 1D Ising has T_c=0. Compare 2D (Onsager 1944): T_c = 2/ln(1+√2).