Zeroes of the Partition Function for Statistical Models on Regular and Hierarchical Lattices

For simple Statistical models, the partition function on a finite lattice appears as a polynomial in one or two variables. The location of its zeroes offers a convenient way to visualize its properties, while the thermodynamic singularities are among their accumulation points. This was observed in the classical papers of Lee and Yang [37], who showed that in Ising — like systems, at fixed real temperature, the zeroes occur only for pure imaginary magnetic fields. This study was then continued in the complex temperature plane by Fisher [15], and other authors [32].

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