Metraipolis › archive › dc_00a8269c0d80

The Arc Threshold of the Two-Row Ising Torus: Exact Factorization, an Algebraic Critical Coupling, Uniformity in the Circumference, and the Rate of Convergence — arXiv:2611.04165

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.04165
License (as archived): CC0-1.0
Archived: 2026-11-04T18:59:52.561Z
SHA-256 of the archived text: ac270fa2a337101bea51721eadcb63dc6e52119da5caeebe4102eaf65be31248
Stable URL of this page: https://metraipolis.com/documento/dc_00a8269c0d80

How to cite

The Arc Threshold of the Two-Row Ising Torus: Exact Factorization, an Algebraic Critical Coupling, Uniformity in the Circumference, and the Rate of Convergence — arXiv:2611.04165 — arXiv (en), https://arxiv.org/abs/2611.04165 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_00a8269c0d80 (Metraipolis archive dc_00a8269c0d80, sha256 ac270fa2a337101bea51721eadcb63dc6e52119da5caeebe4102eaf65be31248)

BibTeX

@misc{dc00a8269c0d80,
  title = {The Arc Threshold of the Two-Row Ising Torus: Exact Factorization, an Algebraic Critical Coupling, Uniformity in the Circumference, and the Rate of Convergence — arXiv:2611.04165},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.04165},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_00a8269c0d80; sha256 ac270fa2a337101bea51721eadcb63dc6e52119da5caeebe4102eaf65be31248},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.04165. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The Lee-Yang circle theorem places every zero of a ferromagnetic Ising partition polynomial on the unit circle. The arc condition, that every zero lie in the closed left half-plane, turns the circle theorem into a product formula for the characteristic function of the occupation count and makes it usable for local limit theorems. For the two-row periodic Ising torus we give the exact reflection factorization of the row transfer matrix, reduce the crossing at zeta = i to a real cubic, and identify the critical coupling a_c* = 0.8637850566870... as the unique root in (0,1) of an explicit octic. We prove that every a > a_c* satisfies the arc condition simultaneously for all circumferences, that no smaller coupling does, and that the finite thresholds approach a_c* at the rate C/n^2 with an explicit algebraic constant C. The factorization and the 2x2 threshold are formalized in Lean 4 against Mathlib; the zeta = i reduction, uniformity and rate are analysis-level.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2611.04165 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T18:37:52.300Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).