Nonconvex optimization methods for ground states in disordered continuous-spin models

This work explores the global optimization problem of finding lowest-energy configurations in disordered continuous-spin models from statistical physics, with a particular focus on the random field XY model. Due to an extremely non-convex nature of the associated energy landscape, this problem remains highly challenging. From an optimization perspective, we reformulate the traditional angular Hamiltonian as a constrained problem on the Cartesian product of spheres, allowing the application of Riemannian optimization techniques, which show better computational performance. We design a family of Basin Hopping algorithms whose perturbation mechanisms are specifically designed to exploit the structure of the underlying physical model, and further extend them within a Population Basin Hopping framework. The proposed methods are evaluated against optimization algorithms widely used in computational physics. The proposed variants turn out to be the most effective method in the comparison, consistently attaining lower-energy configurations within the same computational budget. This work establishes a robust link between continuous-spin systems and continuous global optimization, providing a high-performance benchmark for exploring complex energy landscapes.