Transitions at avoided level crossing with interaction and disorder

We investigate the influence of interaction between tunneling particles and disorder on their avoided-level-crossing transitions in the fast-sweep limit. Whereas the results confirm expectations based on the mean-field arguments that ferromagnetic/antiferromagnetic couplings suppress/enhance transitions, we found large deviations from the mean-field behavior for dipole-dipole interactions (DDI) in molecular magnets Mn-12 and Fe-8. For ideal crystals of the needle, spherical, and disc shapes DDI tends to enhance transitions. This tendency is inverted for the needle shape in the presence of even small disorder in the resonance fields of individual particles, however.