Phase diagram of ferrimagnetic ladders with bond alternation

We study the phase diagram of a two-leg bond-alternation spin-(1/2, 1) ladd er for two different configurations using a quantum renormalization-group a pproach. Although d-dimensional ferrimagnets show gapless behavior, we will explicitly show that the effect of the spin mixing and the bond alternatio n can open the possibility for observing an energy gap. We show that the ga pless phases of such systems can be equivalent to the one-dimensional half- integer antiferromagnets, besides the gapless ferrimagnetic phases. We ther efore propose a phase transition between these two gapless phases that can be seen in the parameter space.