  A path integral method, combined with atomistic spin dynamics simulations,
has been developed to calculate thermal quantum expectation values using a
classical approach. In this study, we show how to treat Hamiltonians with
non-linear terms, that are relevant for describing uniaxial anisotropies and
mechanical constraints. These interactions can be expressed solely through
quadratic terms of the spin operator along one axis, that can be identified
with the quantisation axis.
