Frustrated Heisenberg antiferromagnets:: Fluctuation-induced first order vs. deconfined quantum criticality

Recently it was argued that quantum phase transitions can be radically different from classical phase transitions with, as a highlight, the deconfined critical points exhibiting fractionalization of quantum numbers due to Berry phase effects. Such transitions are supposed to occur in frustrated (J(1)-J(2)) quantum magnets. We have developed a novel renormalization approach for such systems which is fully respecting the underlying lattice structure. According to our findings, another profound phenomenon is around the corner: a fluctuation-induced (order-out-of-disorder) first-order transition. This has to occur for large spin and we conjecture that it is responsible for the weakly first-order behavior recently observed in numerical simulations for frustrated S = 1/2 systems.