  We present a novel mixed-spin cluster expansion method for a
quasi-one-dimensional Haldane system with bond alternation. By mapping the s=1
antiferromagnetic spin model on square and cubic lattices to the equivalent
mixed-spin model, we study the competition among the Haldane, the dimer and the
magnetically ordered phases. The mixed-spin cluster expansion proposed here
allows us to directly deal with the Haldane phase, which may not be reached by
standard series expansion methods. The phase diagram is determined rather
precisely by making use of an additional symmetry property in the effective
mixed-spin model introduced.
