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arXiv:2503.23758 · Physical review. B./Physical review. B

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

Wei‐Guo Yin

Published Aug 26, 2025• 4 citations
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Abstract

The one-dimensional (1D) ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ $q$-state Potts model is solved exactly for arbitrary $q$ by analytically block-diagonalizing the original ${q}^{2}\ifmmode\times\else\texttimes\fi{}{q}^{2}$ transfer matrix into a simple $2\ifmmode\times\else\texttimes\fi{}2$ 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 ${J}_{2}$ acts as the nearest-neighbor interaction and ${J}_{1}$ 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.

DOI
10.1103/y5vc-3t6q

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