Localized to extended states transition for two interacting particles in a two-dimensional random potential

We show by a numerical procedure that a short-range interaction u induces extended two-particle states in a two-dimensional random potential. Our procedure treats the interaction as a perturbation and solve Dyson's equation exactly in the subspace of doubly occupied sites. We consider long bars of several widths and extract the macroscopic localization and correlation lengths by a scaling analysis of the renormalized decay length of the bars. For u=1, the critical disorder found is $W_{\rm c}=9.3\pm 0.2$, and the critical exponent $\nu=2.4\pm 0.5$. For two non-interacting particles we do not find any transition and the localization length is roughly half the one-particle value, as expected