Abstract
In this thesis we investigate the disorder effects on two distinct classes of magnetic systems: itinerant ferromagnets and Heisenberg magnets. In the former case we develop a Replica-Stoner Theory combines Stoner mean-field theory and the replica trick to study the magnetic properties of dirty ferromagnets. The resulting replica-symmetric solution shows that disorder can enhance ferromagnetism or even induce magnetic moments in systems that are non-magnetic in the clean limit. At finite temperatures, a phase diagram including paramagnetic, ferromagnetic, and spin-glass phases is obtained by Landau theory, in which the Curie temperature is enhanced by disorder. For Heisenberg magnets, we study the antiferromagnetic Heisenberg model on the triangular lattice under weak random Zeeman f ields using a modified linear response theory. We find that random fields suppress both the spinon pairing amplitude in the spin-liquid state and the magnetization in the 120-degree Néel state. Together, these studies provide theoretical understandings of how quenched disorder affect magnetic systems in both itinerant ferromagnetism and Heisenberg magnets, offering potential insights into experiments on disordered magnetic materials