Magnetic small world nanomaterials: Physical small-world networks

The question addressed is whether magnetic materials based on physical small-world networks are possible. Physical constraints, such as uniform bond length and embedding in three dimensions, are the features added to make small-world networks physical. Results are presented to further determine if physical small-world networks can exist and the effect of the small-world connections on the critical phenomena of Ising models on such networks. Spectra of the Laplacian on randomly collapsed bead-chain networks are studied. The scaling function for the order parameter of an Ising model with physical small-world connections is presented.