Tunning magnetic phases of Ising systems on continuous networks

Understanding the complex associations between atomic or molecular constituents of materials is essential for conceiving new materials with tailored properties. Researchers use network science to map out and create atomic structures, interactions, and defects in various materials, leading to breakthroughs in designing advanced materials and high-performance composites. We explore the fundamental concepts of the Ising model on a continuous substrate of variable particle density and interaction radius. The magnetic structure consists of N nodes representing spin particles randomly positioned in a unity square area and periodic boundary conditions. We investigate the manifestation of Curie transitions under a tunable local interaction radius, which relates to the spin network's average connectivity〈k〉. Using Monte Carlo simulations, we examine the ferromagnetic evolution and obtain the phase diagram T versus〈k〉and critical exponents. We establish a connection between the emergence of ordered phases in magnetic systems and complex networks and observe that Curie temperature is an increasing function of the local interaction radius.