Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models

Abstract

It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-S Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions. © 1966 The American Physical Society.