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Exact Potts model partition functions on wider arbitrary-length strips of the square 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 for general q and temperature on strips of the square lattice of width Ly=3 vertices and arbitrary length Lx with periodic longitudinal boundary conditions, of the following types: (i) (FBCy,PBCx)= cyclic, (ii) (FBCy,TPBCx)= Möbius, (iii) (PBCy,PBCx)= toroidal, and (iv) (PBCy,TPBCx)= Klein bottle, where FBC and (T)PBC refer to free and (twisted) periodic boundary conditions. Results for the Ly=2 torus and Klein bottle strips are also included. In the infinite-length limit the thermodynamic properties are discussed and some general results are given for low-temperature behavior on strips of arbitrarily great width. We determine the submanifold in the C2 space of q and temperature where the free energy is singular for these strips. Our calculations are also used to compute certain quantities of graph-theoretic interest.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:296:y:2001:i:1:p:234-288
    DOI: 10.1016/S0378-4371(01)00142-X
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    Cited by:

    1. Park, Jae-Hyun, 2017. "Time-dependent reliability of wireless networks with dependent failures," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 47-61.
    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.
    4. 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).

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