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For positive ferromagnetic exchange and nonnegative transverse field, the Ising-chain quasiparticle dispersion closes its gap at $g=1$, with ${ϵ}_k\sim 2J|k|$. This is the quantum phase transition between the model's ordered and field-polarized regimes. The exact dispersion identifies the gapless scale; computing its order parameter additionally requires ground-state correlations.