Evolution and structure formation of the distribution of partition function zeros: triangular type Ising lattices...

The distribution of partition function zeros of the two-dimensional Ising model in the complex temperature plane is studied within the context of triangular decorated lattices and their triangle-star transformations. Exact recursion relations for the zeros are deduced for the description of the evolution of the distribution of the zeros subject to the change of decoration level. In the limit of infinite decoration level, the decorated lattices essentially possess the Sierpiński gasket or its triangle-star transformation as the inherent structure. The positions of the zeros for the infinite decorated lattices are shown to coincide with the ones for the Sierpiński gasket or its triangle-star transformation, and the distributions of zeros all appear to be a union of infinite scattered points and a Jordan curve, which is the limit of the scattered points.