Loading [MathJax]/jax/output/SVG/config.js
Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


TMF:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 220, Number 2, Pages 286–297
DOI: https://doi.org/10.4213/tmf10684 (Mi tmf10684) 		 
Kramers–Wannier duality and Tutte polynomials

A. A. Kazakovabcd

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
b Centre of Integrable Systems, Demidov Yaroslavl State University, Yaroslavl, Russia
c Lobachevsky Institute for Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kazan, Russia
d Center for Fundamental Mathematics, Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region, Russia
Full-text PDF (499 kB) First page
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf10684
Abstract: We study applications of the connection between the partition functions of the Potts models and Tutte polynomials: it is demonstrated how the Kramers–Wannier duality can be derived from the Tutte duality. Using the “contraction–elimination” relation and the Biggs formalism, we derive the high-temperature expansion and discuss possible methods for generalizing the Kramers–Wannier duality to models on nonplanar graphs.
Keywords: Ising model, Potts model, Tutte polynomials, Biggs model, Kramers–Wannier duality.
Funding agency Grant number
Russian Science Foundation 20-71-10110
This work was supported by the Russian Science Foundation (grant No. 20-71-10110, https://rscf.ru/en/project/23-71-50012/), which financially supports the author's research at Demidov Yaroslavl State University.
Received: 30.01.2024
Revised: 25.03.2024
English version:
Theoretical and Mathematical Physics, 2024, Volume 220, Issue 2, Pages 1304–1314
DOI: https://doi.org/10.1134/S0040577924080051
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. A. Kazakov, “Kramers–Wannier duality and Tutte polynomials”, TMF, 220:2 (2024), 286–297; Theoret. and Math. Phys., 220:2 (2024), 1304–1314
Citation in format AMSBIB
\Bibitem{Kaz24}
\by A.~A.~Kazakov
\paper Kramers--Wannier duality and Tutte polynomials
\jour TMF
\yr 2024
\vol 220
\issue 2
\pages 286--297
\mathnet{http://mi.mathnet.ru/tmf10684}
\crossref{https://doi.org/10.4213/tmf10684}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4792095}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2024TMP...220.1304K}
\transl
\jour Theoret. and Math. Phys.
\yr 2024
\vol 220
\issue 2
\pages 1304--1314
\crossref{https://doi.org/10.1134/S0040577924080051}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85202038946}
Linking options:
  • https://www.mathnet.ru/eng/tmf10684
  • https://doi.org/10.4213/tmf10684
  • https://www.mathnet.ru/eng/tmf/v220/i2/p286
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:118
    Full-text PDF :2
    Russian version HTML:3
    References:23
    First page:9
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025