Nonconverging hysteresis cycles in random spin networks.

Behavior of hysteretic trajectories for cyclical input is investigated as a function of the internal structure of a system modeled by the classical random network of binary spins. Different regimes of hysteretic behavior are discovered for different network connectivity and topology. Surprisingly, hysteretic trajectories which do not converge at all are observed. They are shown to be associated with the presence of specific topological elements in the network structure, particularly with the fully interconnected spin groups of size equal to or greater than 4.