Random Ising Hamiltonian Model of Metasurfaces in Complex Environments

The optimisation of Reconfigurable Intelligent Surfaces (RIS) requires tractable channel models that are electromagnetic compliant. We incorporate the effect of multipath fading in an impedance-based model of wireless communication links assisted by the RIS. The multi-path fading present in complex propagation environments is captured by a statistical model based on wave chaos theory: The random coupling model. We show that the so obtained MIMO transfer matrix configures as a Sherrington-Kirkpatrick Hamiltonian with generalised complex-valued Hopfield couplings. For both SISO and MIMO systems, we perform numerical Montecarlo simulations that elucidate the transition to Gaussianity, as parameterised by the average environment losses and RIS line-of-sight channel strengths. Finally, we discuss a research roadmap that includes: i) Retrieving the transmission matrix of complex environments from random coupling fluctuation; ii) Studying of the relation between channel hardening and the onset of a spin-glass phase. Achieved results are important for smart surface environment design.