Half-ice, half-fire driven ultranarrow phase crossover in 1D decorated q-state Potts ferrimagnets: An AI-co-led exploration

OpenAI's reasoning model o3-mini-high was used to carry out an exact analytic study of onedimensional ferrimagnetic site- and bond-decorated q-state Potts models. We demonstrate that the finitetemperature ultranarrow phase crossover (UNPC), driven by a hidden"half-ice, half-fire"state recently discovered in the $q = 2$ case (Ising model), persists for $q>2$. We identify unique novel features for $q>2$, including the dome structure in the field-temperature phase diagram and for large $q$ a secondary high-temperature UNPC to the fully disordered paramagnetic state. Moreover, while the crossover temperature $T_0$ in the site-decorated Potts model is independent of the spin interaction $J$ between the backbone spins and thus remains unchanged as the UNPC quickly approaches a genuine transition -- the crossover width is narrowed exponentially -- by enhancing $J$ (referred to as Type-I UNPC), $T_0$ in the bond-decorated Potts model with $q>2$ depends on $J$ and quickly shifts toward a finite temperature as $J$ increases (referred to as Type-II UNPC). These novel results establish a versatile framework for engineering controlled fast state-flipping switches in low-dimensional systems. Our nine-level AI-contribution rating assigns AI the meritorious status of AI-co-led discovery in this work.