Statistical Mechanics of Alternant Spin Waves

Abstract

The statistical mechanics of the Heisenberg antiferromagnetic ring of doublet sites with alternating exchange coupling is investigated by an approximate method based on the equivalence, established by the Jordan–Wigner transformation, of Pauli spin matrices and Fermi annihilation and creation operators. Mathematically, the theory is somewhat similar to the pseudospin approach of Soos, but the physical interpretation is quite different, being analogous to that in Anderson's theory of antiferromagnetism. Unlike Soos' work, the present formulation requires the sublattice magnetization to vanish at all temperatures, in agreement with the exact result of Mermin and Wagner. Different magnetic susceptibility valves are derived which are in better agreement with the numerical results of Duffy and Barr.