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

We show by a numerical procedure that a short-range interaction u induces e xtended two-particle states in a two-dimensional random potential. Our proc edure treats the interaction as a perturbation and solve Dyson's equation e xactly in the subspace of doubly occupied sites. We consider long bars of s everal widths and extract the macroscopic localisation and correlation leng ths by a scaling analysis of the renormalized decay length of the bars. For u = 1, the critical disorder found is W-c = 9.3 +/- 0.2, and the critical exponent nu = 2.4 +/- 0.5. For two non-interacting particles we do not find any transition and the localization length is roughly half the one-particl e value, as expected.