The energy spectrum of a one-dimensional, exactly solvable spin model formed by two semi-infiniteXYspin chains with spins=1/2with a point-contact interaction in a longitudinal magnetic field is calculated. It is shown that the spectrum of such a system can contain one or two local energy levels apart from two bands overlapping in weak fields. Local thermodynamic parameters of the chains can have singularities at zero temperature. ©1998 American Institute of Physics.