Luca Maria Del Bono — Sapienza Università di Roma #
The de-Almeida Thouless line of sparse isotropic Heisenberg spin glasses #
Results regarding spin glass models are, to this day, mainly confined to models of Ising spins. Models of continuous spins, which exhibit interesting new physics connected to the additional degrees of freedom, have  primarily been studied on fully connected topologies. Only recently some advancements have been made in the study of continuous models on sparse graphs. 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 the model and the critical field at zero temperature and show the full consistency of the methods presented.  Aside from these results, the approaches presented can be applied in the much broader context of studying Heisenberg spin glasses. They can therefore be used as a stepping stone to study further the behavior of these systems, thus helping to gain a better understanding of continuous models of spin glasses.