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Dimer statistics on the Klein bottle

Author

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  • Lu, Fuliang
  • Zhang, Lianzhu
  • Lin, Fenggen

Abstract

The problem of enumerating close-packed dimers, or perfect matchings, on a quadratic lattice embedded on the Klein bottle is considered. Thomassen [C. Thomassen, Tilings of the torus and the Klein Bottle and vertex-transitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323(2) (1991) 605–635] characterized that there are six quadrilateral lattices embedded on the Klein bottle. Lu and Wu [W. T. Lu and F. Y. Wu, Close-packed dimers on nonorientable surfaces, Phys. Lett. A 293 (2002) 235–246] had obtained a expression for the number of close-packed dimers on one of them. In this paper we investigate four other embeddings and obtain explicit expressions of the numbers of close-packed dimers and free energy per dimer by enumerating Pfaffians.

Suggested Citation

  • Lu, Fuliang & Zhang, Lianzhu & Lin, Fenggen, 2011. "Dimer statistics on the Klein bottle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2315-2324.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:12:p:2315-2324
    DOI: 10.1016/j.physa.2011.02.038
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    References listed on IDEAS

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    1. Yan, Weigen & Yeh, Yeong-Nan & Zhang, Fuji, 2008. "Dimer problem on the cylinder and torus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6069-6078.
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    Cited by:

    1. Li, Wei & Zhang, Heping, 2012. "Dimer statistics of honeycomb lattices on Klein bottle, Möbius strip and cylinder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3833-3848.
    2. Guenther-Lübbers, Welf & Arens, Ludwig & Theuvsen, Ludwig, 2013. "Climate-Adapted Soil Cultivation as an Aspect for Sustainable Farming – Task-Technology-Fit of a Decision Support System," International Journal on Food System Dynamics, International Center for Management, Communication, and Research, vol. 4(1), pages 1-9, July.

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