  We study phase transitions in a two dimensional weakly interacting Bose gas
in a random potential at finite temperatures. We identify superfluid, normal
fluid, and insulator phases and construct the phase diagram. At T=0 one has a
tricritical point where the three phases coexist. The truncation of the energy
distribution at the trap barrier, which is a generic phenomenon in cold atom
systems, limits the growth of the localization length and in contrast to the
thermodynamic limit the insulator phase is present at any temperature.

Disordered Systems and Neural Networks;Quantum Gases