Analyticity properties of the Ising model in the antiferromagnetic phase

The partition function of the Ising antiferromagnet is proved to have no zeroes in an annulus around the origin in the complexz-plane. The intersection of this annulus with the positive real axis belongs to the antiferromagnetic region. The free energy and the correlation functions are analytic in the annulus.On leave of absence from the University of Groningen, the Netherlands; supported by the Netherlands Organization for Pure Scientific Research (Z.W.O.).Supported by the National Swiss Foundation for Scientific Research.