H = J Σ (S^x_i S^x_{i+1} + S^y_i S^y_{i+1} + Δ S^z_i S^z_{i+1}). Exact Bethe ansatz solution. Explore the phase diagram: ferromagnet (Δ<-1), critical/XY phase (-1<Δ<1), Néel antiferromagnet (Δ>1).
XXZ chain: exactly solvable by Bethe ansatz (Orbach 1958). Phase diagram: Δ<-1: ferromagnet (gapped, long-range order along z); -1<Δ<1: critical XY (gapless, algebraic correlations, central charge c=1 CFT); Δ>1: Néel antiferromagnet (gapped, staggered order). At Δ=-1: ferromagnet; Δ=0: XX model (free fermions, Jordan-Wigner); Δ=1: isotropic Heisenberg (c=1 WZW). Quantum phase transition at Δ=±1.