A Note on the Ground State of Antiferromagnetism

抄録

Kasteleijn’s method of obtaining the ground state of antiferromagnetism is generalized to the cases of two and three dimensional lattices. According to our generalization, the ground state of the three dimensional antiferromagnetic Heisenberg model with the spin quantum number equal to one half is paramagnetic in the absence of anisotropy energy. The magnetization of sublattices is calculated as a function of the degree of anisotropy. With increasing coordination numbers the anisotropy energy necessary for establishing the antiferromagnetic state decreases rapidly.