O(3) nonlinear model and the topological distinction between integer- and half-integer-spin antiferromagnets in two dimensions

It is shown that the O(3) nonlinear model derived from the quantum Heisenberg antiferromagnet in two spatial dimensions, under the assumption that the Néel field (r,t) is well defined at all points in (2+1)D space-time, has no Hopf term, in contradiction to recent speculation. However, the amplitudes for tunneling between configurations with different spatial topologies reveal a difference between integer and half-integer, and between even- and odd-integer, spins.