Using exact results, we determine the complex-temperature phase diagrams of the 2D Ising model on three regular heteropolygonal lattices, (188.8.131.52) (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 Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics