Qualitative study of the boundary correlation function in the two-dimensional XY-model

The two-point correlation function at the rectilinear boundary of the two-dimensional half-space is studied for the XY-model for the case of free boundary conditions. It is shown that defects of vortex-type at the boundary form a one-dimensional plasma for T ≠ 0, but that this does not lead to exponential decay of the boundary correlation function for T < T_c^bulk.