Minicourse on disorder and dynamics in strongly correlated materials

One surprising phenomenon in frustrated magnets is the order-by-disorder mechanism: thermal and/or quantum fluctuations lift a macroscopic accidental degeneracy of the classical ground state of frustrated magnets. The resulting magnetically ordered-by-(thermal/quantum)disorder state often breaks a real-space symmetry of the crystal lattice. In this talk, we use symmetry arguments, perturbation theory, and Monte Carlo simulations to pedagogically introduce the order by disorder mechanism on the J1-J2 Heisenberg model on a square lattice and to the easy-plane pyrochlores. In addition, we investigate the effects of impurities (vacancies, chemical doping, etc.) on the resulting ordered state. Because inhomogeneities generically break real-space symmetries, it couples to the order-parameter as a conjugate field. Consequently, non-perturbative effects destabilize the ordered-by-disorder state at sufficiently low dimensions preempting any phase transition.