Distribution of zeros of the partition function of the antiferromagnetic Husimi-Temperley model I

To study the locus of zeros of the partition function for the antiferromagnets, an exactly soluble simplest model (the antiferromagnetic Husimi-Temperley model) is proposed. Thermodynamic properties of the model are shown to be the same as those in the molecular field approximation of the Ising or Heisenberg model. The locus of zeros in the complex fugacity plane of the model is obtained by the method of comparing the real part of the various branches of the complex free energies. The locus is a loop which does not cut the real positive axis above the critical temperature. Below the critical temperature, the locus of the zeros consists of dual loops which cut the real positive axis at z c and 1/z c and the density of zeros near the real axis is proportional to mod z-z c mod . At the critical temperature the locus is a loop which crosses at z=1 and the density of zeros is proportional to mod z-z c mod 3 .