Frustrated magnetic systems are characterized by competing interactions that in some cases prevent conventional magnetic ordering, leading to unconventional ground states such as quantum and classical spin liquids. These states exhibit strong entanglement, fractional- ized excitations, and emergent topological phenomena. Such systems are of interest not only from a theoretical perspective, due to their rich and unconventional physics, but also from a materials standpoint, as they offer promising platforms for realizing exotic phases in real compounds. The theoretical study of magnetic models using numerical methods plays a crucial role in advancing our understanding of the magnetic properties of materials. It helps interpret experimental results, predicts properties not yet explored experimentally, and enhances the interpretation of data through the development of new numerical tools. In this thesis, we address these aspects through three main investigations. First, we study classical spin models on the distorted windmill lattice, which is relevant to the spin-liquid candidate PbCuTe2O6. Through this study, we determine the origin of frustration in this compound and examine the thermodynamic behavior and the magnetic excitations of the associated classical model. Additionally, by mapping out the classical phase diagram, we identify a novel type of classical spin liquid. Next, we investigate the dynamical signatures of soft modes, focusing on quartic spin oscillations in isotropic systems with spiral magnetic order. We show that these modes exhibit a gap that decreases with temperature, a feature observable in real materials through inelastic neutron scattering experiments. Finally, we introduce a machine learning–based approach to infer the underlying magnetic Hamilto- nian. Specifically, we train a neural network on synthetic spectra generated using linear spin-wave theory and apply the trained model to analyze experimental inelastic neutron scattering spectra.
