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Partition function zeros for the two-dimensional Ising model II

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  • Stephenson, John

Abstract

The distribution of complex temperature zeros of the partition function of the two-dimensional Ising model in the absence of a magnetic field is investigated in detail for a general anisotropic triangular lattice. When the three Ising interactions are all different the explicit expression for the distribution function obtained is valid near both the ferro- and antiferromagnetic critical points, and has the same mathematical form as for the anisotropic quadratic lattice. In the special case when the strongest interaction is antiferromagnetic and the two weaker interactions are equal, the distribution of zeros is radially symmetric around the antiferromagnetic zero temperature point (in the appropriate complex variable plane), except for a narrow cusp-like region near the real axis, and yields an unusual specific heat behaviour in (inevitable) agreement with the (novel?) thermodynamic results.

Suggested Citation

  • Stephenson, John, 1986. "Partition function zeros for the two-dimensional Ising model II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 136(1), pages 147-159.
    • Handle: RePEc:eee:phsmap:v:136:y:1986:i:1:p:147-159
    DOI: 10.1016/0378-4371(86)90047-6
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