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Atomistic simulations of thermodynamic properties of magnetic materials relyon an accurate modelling of magnetic interactions and an efficient sampling ofthe high-dimensional spin space. Recent years have seen significant progresswith a clear trend from model systems to material specific simulations that areusually based on electronic-structure methods. Here we develop a HamiltonianMonte Carlo framework that makes use of auxiliary spin-dynamics and anauxiliary effective model, the temperature-dependent spin-cluster expansion, inorder to efficiently sample the spin space. Our method does not require aspecific form of the model and is suitable for simulations based onelectronic-structure methods. We demonstrate fast warm-up and a reasonablysmall dynamical critical exponent of our sampler for the classical Heisenbergmodel. We further present an application of our method to the magnetic phasetransition in bcc iron using magnetic bond-order potentials.

Accelerating spin-space sampling by auxiliary spin-dynamics and temperature-dependent spin-cluster expansion