H = J Σᵢ [SˣᵢSˣᵢ₊₁ + SʸᵢSʸᵢ₊₁ + ΔSᶻᵢSᶻᵢ₊₁] − h Σᵢ Sᶻᵢ

Phase diagram:
Δ < −1: Ferromagnetic (FM)
−1 < Δ < 1: Luttinger liquid (LL)
Δ > 1: Antiferromagnetic (AF)
Δ = ±1: BKT transitions

The spin chain is exactly solvable via Bethe ansatz. The LL phase has power-law correlations; the AF phase has long-range Néel order and a gap.