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We show that the two-dimensional (12D) Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all its spin-spin coupling equal to iπ4 and all parameters of the original model are contained in the local magnetic fields of the Ising model. This result has already been derived by using techniques from quantum information theory and by exploiting the universality of cluster states. Here we do not use the quantum formalism and hence make the completeness result accessible to a wide audience. Furthermore, our method has the advantage of being algorithmic... 

Very recently, two-dimensional (2D) iodinene, a novel layered and buckled structure has been successfully fabricated (Qian et al 2020 Adv. Mater. 32 2004835). Motivated by this latest experimental accomplishment, for the first time we conduct density functional theory, first-principles calculations to explore the structural, electronic, and optical properties of monolayer, few-layer and bulk iodinene. Unlike the majority of monoelemental 2D lattices, iodinene is predicted to be an intrinsic semiconductor. On the basis of calculations using the generalized gradient approximation of Perdew-Burke-Ernzerhof for the exchange-correlation functional and the Heyd-Scuseria-Ernzerhof (HSE06)...