  We introduce a two-dimensional short-range correlated disorder that is the
natural generalization of the well-known one-dimensional dual random dimer
model [Phys. Rev. Lett 65, 88 (1990)]. We demonstrate that, as in one
dimension, this model induces a localization-delocalization transition in the
single-particle spectrum. Moreover we show that the effect of such a disorder
on a weakly-interacting boson gas is to enhance the condensate spatial
homogeneity and delocalisation, and to increase the condensate fraction around
an effective resonance of the two-dimensional dual dimers. This study proves
that short-range correlations of a disordered potential can enhance the quantum
coherence of a weakly-interacting many-body system.
