Symplectic integrators for spin systems

We present a symplectic integrator, based on the implicit midpoint method, for classical spin systems where each spin is a unit vector in R³. Unlike splitting methods, it is defined for all Hamiltonians and is O (3)-equivariant, i.e., coordinate-independent. It is a rare example of a generating function for symplectic maps of a noncanonical phase space. It yields a new integrable discretization of the spinning top.