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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Functional Relations on Anisotropic Potts Models: from Biggs Formula to the Tetrahedron Equation
Boris Bychkovab, Anton Kazakovabc, Dmitry Talalaevbca a Centre of Integrable Systems, P.G. Demidov Yaroslavl State University,
Sovetskaya 14, 150003, Yaroslavl, Russia
b Faculty of Mathematics, National Research University Higher School of Economics,
Usacheva 6, 119048, Moscow, Russia
c Faculty of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia
Аннотация:
We explore several types of functional relations on the family of multivariate Tutte polynomials: the Biggs formula and the star-triangle ($Y-\Delta$) transformation at the critical point $n=2$. We deduce the theorem of Matiyasevich and its inverse from the Biggs formula, and we apply this relation to construct the recursion on the parameter $n$. We provide two different proofs of the Zamolodchikov tetrahedron equation satisfied by the star-triangle transformation in the case of $n=2$ multivariate Tutte polynomial, we extend the latter to the case of valency 2 points and show that the Biggs formula and the star-triangle transformation commute.
Ключевые слова:
tetrahedron equation, local Yang–Baxter equation, Biggs formula, Potts model, Ising model.
Поступила: 6 июля 2020 г.; в окончательном варианте 26 марта 2021 г.; опубликована 7 апреля 2021 г.
Образец цитирования:
Boris Bychkov, Anton Kazakov, Dmitry Talalaev, “Functional Relations on Anisotropic Potts Models: from Biggs Formula to the Tetrahedron Equation”, SIGMA, 17 (2021), 035, 30 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1718 https://www.mathnet.ru/rus/sigma/v17/p35
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