An Integrable Classical Spin Chain

An integrable spin model on the one-dimensional lattice is obtained from the differential-difference nonlinear Schrödinger equation by introducing the concept of gauge equivalence. The Hamiltonian for this spin model is expressed as \begin{aligned} H{=}-2\sum_{n}{\log}(1+\textbf{\itshape S}_{n}\cdot \textbf{\itshape S}_{n+1}) \end{aligned} where the spins S n are classical three-dimensional unit vectors.