  There is a large amount of evidence that the ABJM model is integrable in the
planar limit. Less clear is whether or not the ABJ model is integrable. Here we
investigate a limit of the ABJ model in the weak coupling limit where one 't
Hooft parameter is much greater than the other. At the 4 loop level in the
SU(2) x SU(2) sector the anomalous dimensions of single trace operators map to
two Heisenberg spin chains with nearest neighbor interactions with an overall
coefficient that is a function of one of the 't Hooft parameters. We conjecture
the form of this function and show that is consistent with observations about
the ABJ model concerning unitarity and parity, including strong coupling
statements.
