Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911177305489408 |
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| author | Yin, Weiguo |
| author_facet | Yin, Weiguo |
| contents | The one-dimensional (1D) $J_1$-$J_2$ $q$-state Potts model is solved exactly for arbitrary $q$ by analytically block-diagonalizing the original $q^2\times q^2$ transfer matrix into a simple $2\times 2$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23758 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping Yin, Weiguo Statistical Mechanics Mathematical Physics The one-dimensional (1D) $J_1$-$J_2$ $q$-state Potts model is solved exactly for arbitrary $q$ by analytically block-diagonalizing the original $q^2\times q^2$ transfer matrix into a simple $2\times 2$ 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. |
| title | Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2503.23758 |