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

Abstract

OpenAI's reasoning model o3-mini-high was used to carry out an exact analytic study of one-dimensional ferrimagnetic site- and bond-decorated $q$-state Potts models. We demonstrate that the finite-temperature ultranarrow phase crossover (UNPC), driven by a hidden "half-ice, half-fire" state recently discovered in the $q=2$ case (Ising model), persists for $q>2$. Moreover, we identify unique 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. As the UNPC quickly approaches a genuine transition by enhancing $J$, the interaction between the backbone spins, two distinct behaviors emerge: In the site-decorated Potts model, $T_0$ is independent of $J$ and thus remains unchanged (Type-I UNPC), and in the bond-decorated Potts model with $q>2$, $T_0$ depends on $J$ and quickly shifts toward a finite temperature as $J$ increases (Type-II UNPC). These results establish a versatile framework for engineering controlled fast state-flipping switches in low-dimensional systems. Our nine-dan artificial intelligence (AI)-contribution framework assigns AI the meritorious status of AI-co-led discovery in this work.

The version accepted for publication, with refined introduction and Appendix A. 9 pages, 7 figures. A sequel to arXiv:2502.11270 and arXiv:2503.23758, a precursor to arXiv:2511.06442. The code and data that support the findings of this article are openly available at https://community.wolfram.com/groups/-/m/t/3489942