1,776 research outputs found
Complex-Temperature Properties of the Ising Model on 2D Heteropolygonal Lattices
Using exact results, we determine the complex-temperature phase diagrams of
the 2D Ising model on three regular heteropolygonal lattices, (kagom\'{e}), , and (bathroom
tile), where the notation denotes the regular -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
plane.Comment: 31 pages, latex, postscript figure
Complex-Temperature Phase Diagram of the 1D Clock Model and its Connection with Higher-Dimensional Models
We determine the exact complex-temperature (CT) phase diagram of the 1D
clock model. This is of interest because it is the first exactly solved system
with a CT phase boundary exhibiting a finite- intersection point where an
odd number of curves (namely, three) meet, and yields a deeper insight into
this phenomenon. Such intersection points occur in the 3D spin 1/2 Ising model
and appear to occur in the 2D spin 1 Ising model. Further, extending our
earlier work on the higher-spin Ising model, we point out an intriguing
connection between the CT phase diagrams for the 1D and 2D clock models.Comment: 10 pages, latex, with two epsf figure
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