Reply to “Comment on ‘Dynamic correlations in a classical two-dimensional Heisenberg antiferromagnet’ ”

In a recent publication [Wysin and Bishop, Phys. Rev. B 42, 810 (1990)], we incorrectly derived the condition that the wave-vector- and time-dependent dynamic structure function S(q,t) for isotropic Heisenberg magnets should satisfy dS(q,t)/dt${\mathrm{|}}_{\mathrm{t}=0\mathrm{}}$=0. In the preceding Comment by Brown, it has been pointed out that the derivation did not preserve the spin commutation relations. However, the above quantity is correctly determined by a sum of three-point spin correlations, 〈${\mathrm{S}}_{\mathrm{n}}^{\mathrm{x}}$${\mathrm{S}}_{\mathrm{m}}^{\mathrm{y}}$${\mathrm{S}}_{\mathrm{m}\prime }^{\mathrm{z}}$〉, which we show are all identically zero in any number of space dimensions. Therefore, the condition is valid, and indeed implies that a sum of Lorentzians cannot be used to fit the frequency-dependent dynamic correlation function S(q,ω).