Two minimal-variable symplectic integrators for stochastic spin systems.

Abstract

We present two symplectic integrators for stochastic spin systems, based on the classical implicit midpoint method. The spin systems are identified with Lie-Poisson systems in matrix algebras, after which the numerical methods are derived from structure-preserving Lie-Poisson integrators for isospectral stochastic matrix flows. The integrators are thus geometric methods, require no auxiliary variables, and are suited for general Hamiltonians and a large class of stochastic forcing functions. Conservation properties and convergence rates are shown for several single-spin and multispin systems.