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