Ising-spin networks with competing geometric interactions: a new perspective for investigating emergent phenomena in complex materials

The application of mathematical graphs and networks in physics is necessary for adequately representing synthesized complex structures and self-assembled nanomaterials of various emergent architectures. Complex networks endowed by Ising spins at nodes and interactions of different signs and orders supported by the network’s geometry open new horizons in researching such complex materials, particularly by enabling graph theoretic approaches to investigate the interplay of structural complexity and emergent dynamical features. Here, we briefly survey emerging physical phenomena that can be appropriately described within this approach, precisely the geometric frustration, geometry-embedded higher-order interactions, and the altered role of disorder. As a showcase, we study the spin reversal dynamics on the hysteresis loop in Ising spin networks consisting of triangles assembled into three different architectures and triangle-embedded interactions of a random sign. We show how geometric frustration, in conjunction with the topology of an assembly, affects the hysteresis loop shape and spin-activity avalanches during the field-driven magnetisation reversal.