Application of the Faddeev Method to the Three-Spin Deviation Problem for the Heisenberg Model

The three-spin deviation problem for the Heisenberg Hamiltonian is attacked by the Faddeev technique. The fact that the two-particle $t$ matrix is separable facilitates the solution. In one dimension, the resulting equation can be numerically solved to obtain the eigenvalue. In two and three dimensions, integral equations in one vector variable appear, but no progress has so far been made towards their solution.