Statistical Models with a Line of Defect
  The factorization condition for the scattering amplitudes of an integrable model with a line of defect gives rise to a set of Reflection-Transmission equations. The solutions of these equations in the case of diagonal $S$-matrix in the bulk are only those with $S =\pm 1$. The choice $S=-1$ corresponds to the Ising model. We compute the transmission and reflection amplitudes relative to the interaction of the Majorana fermion with the defect and we discuss their relevant features. 
G. Delfino, G. Mussardo and P. Simonetti