Theoretical constraints for the magnetic-dimer transition in two-dimensional spin models

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 semiclassical 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 a four-spin ring-exchange interaction, recently introduced by A.W. Sandvik, S. Daul, R.R.P. Singh, and D.J. Scalapino [Phys. Rev. Lett. 89, 247201 (2002)].