Flux Jamming and Bimodal Dynamics in Bounded Spin Networks

We present a quantitative framework for predicting how kinetic barriers governing temperature dependent relaxation arise in finite square magnetic networks. By formulating a series of non homogeneous transfer matrices from the adjacency spectrum of the underlying graph, we show how local coordination shapes the energy landscape and identifies geometric regions that act as bottlenecks for flux transport. Our approach predicts bimodal kinetic behavior, in which long intervals of trapping within charge compensated manifolds are interrupted by sudden, avalanche like relaxation episodes. Representing finite systems with a Husimi tree, we find that low temperature data from forty generations collapse onto a single curve consistent with a power law scaling form, implying that boundary truncation alone can give rise to scale invariant flux arrest, analogous to athermal granular jamming. By employing transition probabilities constructed from local Boltzmann factors, this framework connects equilibrium energy landscape concepts to non equilibrium phenomena, including kinetic arrest and telegraph noise, thereby enabling the prediction and design of intermittent transport in finite, frustrated networks.