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The Spectrum and Laplacian Spectrum of the Dice Lattice

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Abstract

The dice lattice is the dual lattice of kagomé lattice. Many physical properties on the dice lattice have been studied by physicists, such as Ising model, Glassy dynamics of Josephson arrays, and Lattice Green’s function. In this paper, we derive the spectrum and Laplacian spectrum of the dice lattice with toroidal boundary condition. In addition, we apply our results to obtain the formulae of the number of spanning trees, the Kirchhoff index, and the energy of the dice lattice with toroidal boundary condition.

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Acknowledgments

I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed.

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Authors and Affiliations

  1. School of Mathematical and Computer Sciences, Quanzhou Normal University, Quanzhou, 362000, China

    Shuli Li

  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Shuli Li

  3. School of Sciences, Jimei University, Xiamen, 361021, China

    Weigen Yan & Tao Tian

Authors
  1. Shuli Li
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  2. Weigen Yan
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  3. Tao Tian
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Correspondence to Shuli Li.

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Funding

This study was funded by NSFC (Grant Number: 11171134).

Conflicts of Interest

The authors declare that they have no conflict of interest.

Additional information

The second author was supported in part by NSFC Grant (11171134).

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Li, S., Yan, W. & Tian, T. The Spectrum and Laplacian Spectrum of the Dice Lattice. J Stat Phys 164, 449–462 (2016). https://doi.org/10.1007/s10955-016-1552-6

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  • DOI: https://doi.org/10.1007/s10955-016-1552-6

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