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Exact Potts model partition functions on strips of the honeycomb lattice

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  • Chang, Shu-Chiuan
  • Shrock, Robert

Abstract

We present exact calculations of the partition function of the q-state Potts model on (i) open, (ii) cyclic, and (iii) Möbius strips of the honeycomb (brick) lattice of width Ly=2 and arbitrarily great length. In the infinite-length limit the thermodynamic properties are discussed. The continuous locus of singularities of the free energy is determined in the q plane for fixed temperature and in the complex temperature plane for fixed q values. We also give exact calculations of the zero-temperature partition function (chromatic polynomial) and W(q), the exponent of the ground-state entropy, for the Potts antiferromagnet for honeycomb strips of type (iv) Ly=3, cyclic, (v) Ly=3, Möbius, (vi) Ly=4, cylindrical, and (vii) Ly=4, open. In the infinite-length limit we calculate W(q) and determine the continuous locus of points where it is nonanalytic. We show that our exact calculation of the entropy for the Ly=4 strip with cylindrical boundary conditions provides an extremely accurate approximation, to a few parts in 105 for moderate q values, to the entropy for the full 2D honeycomb lattice (where the latter is determined by Monte Carlo measurements since no exact analytic form is known).

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  • 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.
    • Handle: RePEc:eee:phsmap:v:296:y:2001:i:1:p:183-233
    DOI: 10.1016/S0378-4371(01)00143-1
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    Cited by:

    1. Chang, Shu-Chiuan & Shrock, Robert, 2020. "Asymptotic behavior of acyclic and cyclic orientations of directed lattice graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. 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.
    3. 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.

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