Spin Chain (each row = one RG level)
K' = ½ ln(cosh(2K)) | Fixed points: K=0 (T→∞), K=∞ (T=0)
Block-spin renormalization on the 1D Ising model: group spins in pairs,
integrate out one per block, and renormalize the coupling. Exact result:
K' = ½ ln cosh(2K). The flow has two fixed points: K=0 (high-T disordered phase)
and K=∞ (low-T ordered phase). All finite-K flows to zero — confirming no phase transition
in 1D. The 1D Ising model cannot order at finite temperature (Landau argument), and RG makes
this explicit: the coupling weakens at every coarse-graining step.