Dielectric susceptibility of magnetoelectric thin films with vortex-antivortex dipole pairs

We consider model of quasi-2D magnetoelectric material as XY model for spin system on a lattice with local multiferroic-like interaction of spin and electric polarization vectors. We calculate the contribution of magnetic (spin) vortex-antivortex pairs (which form electric dipoles) to the dielectric susceptibility of the system. We show that in approximation of non-interacting pairs at $T\to T_{BKT}$ (Berezinskii-Kosterlitz-Thouless temperature) dielectric susceptibility diverges.