Delocalization of two-particle ring near the Fermi level of 2d Anderson model

We study analytically and numerically the problem of two particles with a long range attractive interaction on a two-dimensional (2d) lattice with disorder. It is shown that below some critical disorder the interaction creates delocalized coupled states near the Fermi level. These states appear inside well localized noninteracting phase and have a form of two-particle ring which diffusively propagates over the lattice.