Metric Features of a Dipolar Model

Abstract

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.