Plateaux transitions from S-matrices based on SL(2,Z) invariant field theories

A scattering description is proposed for a boundary perturbation of a c=1 SL(2,Z) invariant conformal field theory. The bulk massless S-matrices are of the form of Zamolodchikovʹs staircase model. Using the boundary version of the thermodynamic Bethe ansatz, we show that the boundary free energy goes through a series of integer valued plateaux as a function of system size.