Complex-temperature properties of the Ising model on 2D heteropolygonal lattices
- 21 September 1995
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 28 (18) , 5235-5256
- https://doi.org/10.1088/0305-4470/28/18/014
Abstract
Using exact results, we determine the complex-temperature phase diagrams of the 2D Ising model on three regular heteropolygonal lattices, (3.6.3.6) (kagome), (3.122) and (4.82) (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 magnetization. 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 non-trivial 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.All Related Versions
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