Replication Data for: A metamaterial analog of the ising model

The interaction between microscopic particles has always been a fascinating and intriguing area of science. Direct interrogation of such interactions is often difficult. Structured electromagnetic systems offer a rich toolkit for mimicking and reproducing the key dynamics that governs the microscopic interactions, and thus provide an avenue to explore and interpret the microscopic phenomena. In particular, metamaterials offer the freedom to artificially tailor light-matter coupling and to control the interaction between unit cells in the metamaterial array. Here we demonstrate a terahertz metamaterial that mimics spin-related interactions of microscopic particles in a 2D lattice via complex electromagnetic multipoles scattered within the metamaterial array. Fano resonances featured by distinct mode properties due to strong nearest-neighbor interactions are discussed that draw parallels with the 2D Ising model. Interestingly, a phase transition from single Fano resonance to hyperfine splitting of Fano spectrum is observed by manipulating the 2D interactions without applying external magnetic or electric fields, which provides a potential multispectral platform for applications in super-resolution imaging, biosensing, and selective thermal emission. The dynamic approach to reproduce static interaction between microscopic particles would enable more profound significance in exploring the unknown physical world by the macroscopic analogues.