Interaction of electric charges in (2+1)D magnetic dipole gas

The interaction of electrically charged particles in a dilute gas of point–like magnetic dipoles is studied. We show that the interaction potential at small distances has a linear piece due to overlap of the dipole clouds gathered near electric sources. At large distances the potential becomes of the Coulomb type with non-perturbatively renormalized charge of the test particle. The physical applications of these results are discussed.