We introduce a discrete Hasimoto transform and show it connects the Faddeev-Takhtajan discrete spin chain model with the Ablowitz-Ladik discrete system. This is then used to prove global well-posedness of the Faddeev-Takhtajan spin chain system for data in the support of the Gibbs measure from global well-posedness for the Ablowitz-Ladik system for data in the support of the associated white noise measure. This is joint work with Y. Angelopoulos and R. Killip.