Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping

The one-dimensional (1D) J₁-J₂ q-state Potts model is solved exactly for arbitrary q by analytically block-diagonalizing the original q²×q² transfer matrix into a simple 2×2 maximally symmetric subspace, based on using OpenAI's reasoning model o3-mini-high to exactly solve the $q=3$ case. Furthermore, by matching relevant subspaces, we map the Potts model onto a simpler effective 1D q-state Potts model, where J₂ acts as the nearest-neighbor interaction and J₁ as an effective magnetic field, nontrivially generalizing a 56-year-old theorem previously limited to the simplest case ($q=2$, the Ising model). Our exact results provide insights to phenomena such as atomic or electronic order stacking in layered materials and the emergence of dome-shaped phases in complex phase diagrams. This work is anticipated to fuel both research in 1D frustrated magnets for recently discovered finite-temperature application potentials and the fast moving topic area of AI in science.