Interplay of topological and structural defects in the two-dimensional XY model

We analyze an effect of quenched non-magnetic impurities on properties of the two-dimensional XY model. In particular, we are interested in the interaction between the impurities and topological defects governing the Berezinskii-Kosterlitz-Thouless transition. We make use of two different analytical approaches: the phenomenological theory of topological defects and the Villain model. As a practical illustration of the obtained results a rough estimation of the transition temperature as a function of the concentration of dilution is made and compared to the available Monte Carlo data.