The Three-Magnon Contribution to the Spin Correlation Function in Integer-Spin Antiferromagnetic Chains

The exact form factor for the O(3) non-linear sigma model is used to predict the three-magnon contribution to the spin correlation function, S(q,w), near wavevector q=pi in an integer spin, one-dimensional antiferromagnet. The three-magnon contribution is extrememly broad and extremely weak; the integrated intensity is <2% of the single-magnon contribution.