Self-organised critical states on hysteresis loop of nanonetworks with random geometric interactions

Self-assembled nanostructures with spontaneous scale-invariant dynamics are intensively researched as promising technological materials. Represented by Ising spin networks, they exemplify systems with concealed geometric features that enable higher-order interactions and geometric frustration responsible for collective dynamics. Recent investigations of hysteretic response to the driving field in nanonetworks assembled of triangles have revealed self-organised criticality in distinct universality classes associated with pure pairwise and triangle-based interactions. In this study, we investigate the hysteresis dynamics associated with triangle-based interactions of these nanoassemblies, considering concurrent influence of interaction disorder and demagnetising fields, both of which influence the effects of geometric frustration. With extensive simulations for various assembly structures and a range of parameters and adjusted field driving rates, we demonstrate robust spin-activity avalanches associated with the altered hysteresis-loop shape. Specifically, the demagnetising fields increase magnetisation fluctuations at the linear segments of the loop, chiefly affecting the behaviour of large avalanches. Meanwhile, the disorder increases the number of distinct connectivity classes of spins, thus gradually smoothing the hysteresis steps, reducing the cutoff size of avalanches and stabilising the strength of magnetisation fluctuations caused by the demagnetising field. The avalanche distributions are modified in the cutoff range, whilst the exponents in the scaling region remain close to the original model, depending on the driving rate. These findings confirm robust hysteresis-loop self-organised critical dynamics induced solely by higher-order geometric interactions. Graphical abstract Close-up image of a nanonetwork composed of triangles that have self-assembled under a repulsive potential