  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.
