Theorems on Extended Ising Model with Applications to Dilute Ferromagnetism

It is proved that the zeros of the partition function of an extended Ising model lie on a unit circle in the fugacity plane under certain conditions. Each spin assumes a general value. The key point of the proof is to derive a simple condition sufficient for zeros of polynomials to lie on a unit circle. Conjectured theorems on the Heisenberg model are also discussed.