An efficient geometric integrator for thermostatted anti-/ferromagnetic models

(Anti)-/ferromagnetic Heisenberg spin models arise from discretization of Landau-Lifshitz models in micromagnetic modelling. In many applications it is essential to study the behavior of the system at a fixed temperature. A formulation for thermostatted spin dynamics was given by Bulgac and Kusnetsov, which incorporates a complicated nonlinear dissipation/driving term while preserving spin length. It is essential to properly model this term in simulation, and simplified schemes give poor numerical performance, e. g., requiring an excessively small timestep for stable integration. In this paper we present an efficient, structure-preserving method for thermostatted spin dynamics.