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Potts model partition functions on two families of fractal lattices

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  • Gong, Helin
  • Jin, Xian’an

Abstract

The partition function of q-state Potts model, or equivalently the Tutte polynomial, is computationally intractable for regular lattices. The purpose of this paper is to compute partition functions of q-state Potts model on two families of fractal lattices. Based on their self-similar structures and by applying the subgraph-decomposition method, we divide their Tutte polynomials into two summands, and for each summand we obtain a recursive formula involving the other summand. As a result, the number of spanning trees and their asymptotic growth constants, and a lower bound of the number of connected spanning subgraphs or acyclic root-connected orientations for each of such two lattices are obtained.

Suggested Citation

  • Gong, Helin & Jin, Xian’an, 2014. "Potts model partition functions on two families of fractal lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 143-153.
    • Handle: RePEc:eee:phsmap:v:414:y:2014:i:c:p:143-153
    DOI: 10.1016/j.physa.2014.07.047
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    References listed on IDEAS

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    1. Liao, Yunhua & Fang, Aixiang & Hou, Yaoping, 2013. "The Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4584-4593.
    2. Chang, Shu-Chiuan & Shrock, Robert, 2001. "Exact Potts model partition functions on wider arbitrary-length strips of the square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(1), pages 234-288.
    3. Chang, Shu-Chiuan & Shrock, Robert, 2001. "Exact Potts model partition functions on strips of the honeycomb lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(1), pages 183-233.
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    Cited by:

    1. Gong, Helin & Jin, Xian’an, 2017. "A general method for computing Tutte polynomials of self-similar graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 117-129.

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