RSS feeds
РусскийEnglish
Issue 11, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1985

 / 

December

←  →

Methodological notes


The dimer problem and the Kirchhoff theorem


Application of the Kirchhoff theorem to lattice statistics leads to solution of the two-dimensional dimer problem, earlier obtained by the Pfaffian method. It is shown that the relation between the theory of network of linear resistors and the dimer problem is particularly useful in the threedimensional case. A number of dimer configurations on a decorated diamond lattice is found by calculating spanning trees on the corresponding lattice. The Kirchhoff theorem is proved in the spirit of the combinatorical solution of the Ising model.

Fulltext pdf (470 KB)
Fulltext is also available at DOI: 10.1070/PU1985v028n12ABEH003987
PACS: 05.50.+q, 02.10.Yn, 02.10.Ox, 61.50.Ah (all)
DOI: 10.1070/PU1985v028n12ABEH003987
URL: https://ufn.ru/en/articles/1985/12/c/
Citation: Priezzhev V B "The dimer problem and the Kirchhoff theorem" Sov. Phys. Usp. 28 1125–1135 (1985)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Приезжев В Б «Задача о димерах и теорема Кирхгофа» УФН 147 747–765 (1985); DOI: 10.3367/UFNr.0147.198512c.0747

Cited by (21) ↓ Similar articles (7)

  1. Nurligareev Kh D, Povolotsky A M J. Stat. Mech. 2023 013101 (2023)
  2. Jacobsen Je L, Saleur H J. High Energ. Phys. 2019 (1) (2019)
  3. Alcaraz F C, Brankov J G et al Phys. Rev. E 90 (5) (2014)
  4. Gorsky A, Nechaev S et al Nuclear Physics B 870 55 (2013)
  5. CIUCU Mihai, LIU Yan, YANG Chunxia Kyushu J. Math. 66 291 (2012)
  6. Grigorev S Y, Poghosyan V S, Priezzhev V B J. Stat. Mech. 2009 P09008 (2009)
  7. Brankov J G, Grigorev S Y et al J. Stat. Mech. 2008 P11017 (2008)
  8. Ruelle P J. Stat. Mech. 2007 P09013 (2007)
  9. Grechannikov A V 21 (1) (2006)
  10. Ivashkevich E V, Hu Ch-K Phys. Rev. E 71 (1) (2005)
  11. Read N Phys. Rev. E 70 (2) (2004)
  12. Ivashkevich E V J. Phys. A: Math. Gen. 32 1691 (1999)
  13. Nash Ch, O’ C D Annals Of Physics 273 72 (1999)
  14. Brankov J G 36 5071 (1995)
  15. Ivashkevich E V, Ktitarev D V, Priezzhev V B Physica A: Statistical Mechanics And Its Applications 209 347 (1994)
  16. Priezzhev V B J Stat Phys 74 955 (1994)
  17. Ivashkevich E V J. Phys. A: Math. Gen. 27 3643 (1994)
  18. Kornilov E I, Priezzhev V B Theor Math Phys 98 61 (1994)
  19. Hayn R, Plechko V N J. Phys. A: Math. Gen. 27 4753 (1994)
  20. Priezzhev V B Phys. Scr. T49B 663 (1993)
  21. Bhattacharjee S M Z. Physik B - Condensed Matter 82 323 (1991)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions