  Atomistic simulations of thermodynamic properties of magnetic materials rely
on an accurate modelling of magnetic interactions and an efficient sampling of
the high-dimensional spin space. Recent years have seen significant progress
with a clear trend from model systems to material specific simulations that are
usually based on electronic-structure methods. Here we develop a Hamiltonian
Monte Carlo framework that makes use of auxiliary spin-dynamics and an
auxiliary effective model, the temperature-dependent spin-cluster expansion, in
order to efficiently sample the spin space. Our method does not require a
specific form of the model and is suitable for simulations based on
electronic-structure methods. We demonstrate fast warm-up and a reasonably
small dynamical critical exponent of our sampler for the classical Heisenberg
model. We further present an application of our method to the magnetic phase
transition in bcc iron using magnetic bond-order potentials.
