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Root-of-unity limit of the $A_{n-1}$ lens elliptic gamma function solution of the star-star relation — arXiv:2610.41438

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41438
License (as archived): CC0-1.0
Archived: 2026-11-03T08:28:28.289Z
SHA-256 of the archived text: cddeba74ca2c69cf0807ce122865aad70f5fe8b82774ccee0ae90e14251c3282
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How to cite

Root-of-unity limit of the $A_{n-1}$ lens elliptic gamma function solution of the star-star relation — arXiv:2610.41438 — arXiv (en), https://arxiv.org/abs/2610.41438 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ce99055f63dd (Metraipolis archive dc_ce99055f63dd, sha256 cddeba74ca2c69cf0807ce122865aad70f5fe8b82774ccee0ae90e14251c3282)

BibTeX

@misc{dcce99055f63dd,
  title = {Root-of-unity limit of the $A_n-1$ lens elliptic gamma function solution of the star-star relation — arXiv:2610.41438},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41438},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ce99055f63dd; sha256 cddeba74ca2c69cf0807ce122865aad70f5fe8b82774ccee0ae90e14251c3282},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41438. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the root-of-unity limit of the multi-component spin solution of the star-star relation whose Boltzmann weights are products of lens elliptic gamma functions, and whose spins take values in $\mathbb{R}^{n-1}\times(\mathbb{Z}_r)^{n-1}$. When one of the elliptic nomes tends to a primitive $2rN$-th root of unity, the quasi-classical expansion gives at leading order the classical star-star relation of the Bazhanov-Sergeev multi-spin model; at the next order, under the standard assumptions on the saddle points, a $(\mathbb{Z}_{rN})^{n-1}$-state solution of the star-star relation, which depends on $r$ and $N$ only through $rN$. Real $\mathbb{Z}_n$-symmetric configurations of the continuous spins give elliptic $\mathfrak{sl}(n)$ Kashiwara-Miwa type models labeled by $n$-torsion points. Extended to general primitive torsion points, these include the broken $\mathbb{Z}_{rN}$ model of Quano and Fujii, for which the star-star relation follows from their Yang-Baxter equation when $\gcd(n,rN)=1$. In the trigonometric limit the saddle point equations single out the spectral curve of the $\mathfrak{sl}(n)$ chiral Potts model of Bazhanov, Kashaev, Mangazeev and Stroganov, and the Boltzmann weights become those of that model.

Tema degli esploratori: fisica e astronomia (elenco arXiv cond-mat.stat-mech, nuovi lavori del giorno).
Categorie arXiv: Mathematical Physics (math-ph) ; Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Exactly Solvable and Integrable Systems (nlin.SI).
Pagina del lavoro: https://arxiv.org/abs/2610.41438 — 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 2026-11-03T08:09:53.779Z dalla pagina https://arxiv.org/list/cond-mat.stat-mech/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).