title: Symplectic integrators for spin systems.
abstract: We present a symplectic integrator, based on the implicit midpoint method, for classical spin systems where each spin is a unit vector in R{3}. 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.
authors.affiliation: Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand.
authors.forename: Robert I
authors.initials: RI
authors.lastname: McLachlan
authors.affiliation: Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden.
authors.forename: Klas
authors.initials: K
authors.lastname: Modin
authors.affiliation: Mathematics and Mathematical Statistics, UmeåUniversitet, SE-901 87 Umeå, Sweden.
authors.forename: Olivier
authors.initials: O
authors.lastname: Verdier
mesh_terms: D008962:Models, Theoretical