Zeros of the Grand Partition Function for a Lattice Gas

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Abstract
The following three statements about the zeros of the grand partition function of a lattice gas with negative (attractive) interactions are proved: (1) Not all the zeros will be on the unit circle in the high‐temperature limit if forces of higher order than 2‐body are included; (2) in the low‐temperature limit they will, in general, lie on the unit circle; (3) it is possible to have the zeros dense in the complex plane. It is also shown that not all polynomials with positive coefficients and roots on the unit circle are a grand partition function of a lattice gas.

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