From disorder to order and back again

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 and Monte Carlo simulations to investigate the effects of impurities (vacancies, chemical doping, etc.). Because inhomogeneities generically break real-space symmetries, it couples to the order-parameter as a conjugate field. As a consequence, inhomogeneities are responsible for non-perturbative effects that destabilize an ordered-by-disorder state at sufficiently low dimensions. As an example, we apply our theory to the J1-J2 Heisenberg model on a square lattice and to the easy-plane pyrochlores.