Non-converging hysteretic cycles in random spin networks

TL;DR

This paper investigates hysteretic behavior in random spin networks, revealing various regimes and discovering non-converging cycles linked to specific topological features like fully interconnected spin groups.

Contribution

It uncovers new hysteretic regimes and identifies topological structures responsible for non-converging cycles in random spin networks.

Findings

Different hysteretic regimes depend on network connectivity and topology.

Non-converging hysteretic cycles are associated with fully interconnected spin groups of size ≥ 4.

Topological elements influence the stability of hysteretic trajectories.

Abstract

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 or greater than 4.