Metric features of a dipolar model

The lattice spin model, with nearest-neighbour ferromagnetic exchange and dipolar interaction, is studied by the method of time series for observables based on cluster configurations and associated partitions, such as Shannon entropy or 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 and related indicators we obtain strong indications that the first one is a true phase transition, corresponding to a particular melting process of oriented domains, where coloured noise is present almost independently of true fractality. The second one, in contrast, seems not to be a true transition. 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 cluster chaotic phase. Comparison with the nearest-neighbour Ising ferromagnetic system reveals a substantial difference in the cluster geometrical properties of the two models and in their critical behaviour