  From general arguments, that are valid for spin models with sufficiently
short-range interactions, we derive strong constraints on the excitation
spectrum across a continuous phase transition at zero temperature between a
magnetic and a dimerized phase, that breaks the translational symmetry. From
the different symmetries of the two phases, it is possible to predict, at the
quantum critical point, a branch of gapless excitations, not described by
standard semi-classical approaches. By using these arguments, supported by
intensive numerical calculations, we obtain a rather convincing evidence in
favor of a first-order transition from the ferromagnetic to the dimerized phase
in the two-dimensional spin-half model with four-spin ring-exchange
interaction, recently introduced by A.W. Sandvik et al. [Phys. Rev. Lett. 89,
247201 (2002)].
