Complex-Temperature Properties of the Ising Model on 2D Heteropolygonal Lattices

Details Complex-Temperature Properties of the Ising Model on 2D Heteropolygonal Lattices Complex-Temperature Properties of the Ising Model on 2D Heteropolygonal Lattices

1995-03-06

arxiv.org/abs/hep-lat/9503005v1

J.Phys. A28 (1995) 5235-5356

Physics

High Energy Physics

High Energy Physics - Lattice

31 pages, latex, postscript figures

Scientific paper

10.1088/0305-4470/28/18/014

Using exact results, we determine the complex-temperature phase diagrams of the 2D Ising model on three regular heteropolygonal lattices, $(3 \cdot 6 \cdot 3 \cdot 6)$ (kagom\'{e}), $(3 \cdot 12^2)$, and $(4 \cdot 8^2)$ (bathroom tile), where the notation denotes the regular $n$-sided polygons adjacent to each vertex. We also work out the exact complex-temperature singularities of the spontaneous magnetisation. A comparison with the properties on the square, triangular, and hexagonal lattices is given. In particular, we find the first case where, even for isotropic spin-spin exchange couplings, the nontrivial non-analyticities of the free energy of the Ising model lie in a two-dimensional, rather than one-dimensional, algebraic variety in the $z=e^{-2K}$ plane.

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