  The lattice spin model, with nearest neighbor ferromagnetic exchange and long
range dipolar interaction, is studied by the method of time series for
observables based on cluster configurations and associated partitions, such as
Shannon entropy, Hamming and Rohlin distances. Previous results based on the
two peaks shape of the specific heat, suggested the existence of two possible
transitions. By the analysis of the Shannon entropy we are able to prove that
the first one is a true phase transition corresponding to a particular melting
process of oriented domains, where colored noise is present almost
independently of true fractality. The second one is not a real transition and
it may be ascribed to a smooth balancing between two geometrical effects: a
progressive fragmentation of the big clusters (possibly creating fractals), and
the slow onset of a small clusters chaotic phase. Comparison with the nearest
neighbor Ising ferromagnetic system points out a substantial difference in the
cluster geometrical properties of the two models and in their critical
behavior.
