Site-decorated model for unconventional frustrated magnets: Ultranarrow phase crossover and two-dimensional spin reversal transition

The site-decorated Ising model is introduced to advance the understanding and experimental realization of the recently discovered one-dimensional (1D) finite-temperature ultranarrow phase crossover in an external magnetic field, while mitigating the geometric complexities of traditional bond-decorated models. The unconventional frustration and physics are clarified by exactly mapping the 1D site-decorated Ising model in a magnetic field onto a zero-field bond-decorated $J_1$-$J_2$ Ising model with conventional geometrical frustration. Furthermore, although higher-dimensional Ising models in an external field remain unsolved exactly, an exact solution for a spin-reversal transition -- driven by an exotic, hidden half-ice, half-fire state induced by site decoration -- is derived. This transition, triggered by a slight variation in temperature or magnetic field -- without changing its direction -- even in the weak-field limit, offers a promising route toward energy-efficient applications such as data storage and processing. The results suggest that site decoration offers an avenue for materials and device design, particularly in systems such as mixed $d$-$f$ compounds, optical lattices, and neural networks, calling for further studies with site-decorated Heisenberg models. In addition, the site-decorated model offers a rigorous test ground for artificial intelligence (AI) in science, as the analytic derivation of the present results was not only validated but also improved by a general-purpose large language model, inspiring the use of AI as scientific discoverer.