  Results regarding spin glass models are, to this day, mainly confined to
models with Ising spins. Spin glass models with continuous spins exhibit
interesting new physical behaviors related to the additional degrees of
freedom, but have been primarily studied on fully connected topologies. Only
recently some advancements have been made in the study of continuous models on
sparse graphs. In this work we partially fill this void by introducing a method
to solve numerically the Belief Propagation equations for systems of Heisenberg
spins on sparse random graphs via a discretization of the sphere. We introduce
techniques to study the finite-temperature, finite-connectivity case as well as
novel algorithms to deal with the zero-temperature and large connectivity
limits. As an application, we locate the de Almeida-Thouless line for this
class of models and the critical field at zero temperature, showing the full
consistency of the methods presented. Beyond the specific results reported for
Heisenberg models, the approaches presented in this paper have a much broader
scope of application and pave the way to the solution of strongly disordered
models with continuous variables.
