  The emergence of self-sustained clusters and their role in ergodicity
breaking is investigated in fully connected Ising and Sherrington-Kirkpatick
(SK) models. The analysis reveals a clustering behavior at various parameter
regimes, as well as yet unobserved phenomena such as the absence of non-trivial
clusters in the Ising ferromagnetic and paramagnetic regimes, the formation of
restricted spin clusters in SK spin glass and a first order phase transition in
cluster sizes in the SK ferromagnet. The method could be adapted to investigate
other spin models.
