  Numerical and theoretical studies of a one-dimensional spin model with
locally broken spin symmetry are presented. The multi-species annihilating
random walk transition found at zero branching rate previously is investigated
now concerning the cluster behaviour of the underlying spins. Generic power law
behaviors are found, besides the phase transition point, also in the active
phase with fulfillment of the hyperscaling law. On the other hand scaling laws
connecting bulk- and cluster exponents are broken - a possibility in no
contradiction with basic scaling assumptions because of the missing absorbing
phase.
