  We consider the anomalous dimensions of restricted Schur polynomials
constructed using n~O(N) complex adjoint scalars Z and m complex adjoint
scalars Y. We fix m<<n so that our operators are almost half BPS. At leading
order in m/n this system corresponds to a dilute gas of m free magnons. Adding
the first correction of order m/n to the anomalous dimension, which arises at
two loops, we find non-zero magnon interactions. The form of this new operator
mixing is studied in detail for a system of two giant gravitons with four
strings attached.
