Nonanalytic correlation length in Ising systems with one surface defect line

A two-dimensional Ising system with ferromagnetic coupling and one defect line at distance L from the surface is solved exactly using Pfaffians. The system shows a singularity in the surface correlation length at a temperature T_s which is smaller than the transition temperature T_c of the bulk. Numerical studies using the transfer matrix technique suggest that this singularity is also present in an Ising system with two defect lines at distance L.