Necessity and Experimental Consistency of Antiferromagnetic Ground State without Long-Range Order

A proof is given that long-range order measured as the average value of the $z$ component of sublattice magnetization of an antiferromagnet must be zero in the exact ground state if that state is nondegenerate and the Hamiltonian is invariant under time reversal. The neutron diffraction magnetic cross section is shown not to depend on such a measure of long-range order.