In this internship project we study how randomness—dilution, substitutions, defects—reshapes phases and observables in prototypical classical and quantum spin models (Ising, Heisenberg, spin ice, loop models). Using analytical and numerical tools (e.g., strong-disorder RG, Monte Carlo), the project will probe density of states, magnetization, specific heat, susceptibility, and especially whether disorder triggers new phase transitions and universality classes. A PhD continuation could focus on sign-problem-resistant algorithms for frustrated quantum magnets, classical statistical descriptions of topological orders/spin liquids, and dynamics of random spin systems.