Rigorous Results for Ising Ferromagnets of Arbitrary Spin

Abstract

The following results for spin-½ Ising ferromagnets are extended to the case of arbitrary spin: (1) the theorem of Lee and Yang, that the zeros of the partition function lie on the unit circle in the complex fugacity plane; (2) inequalities of the form ≥ , where A and B are products of spin operators; (3) the existence of spontaneous magnetization on suitable lattices. Results (2) and (3) are also extended to the infinite-spin limit in which the spin variable is continuous on the interval −1 ≤ x ≤ 1.