Abstract
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.
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