BEC in two dimensions with interactions For noninteracting 2D system of bosons, many textbooks have a statement that no BEC exists as the system is capable to accommodate infinite number of bosons when chemical potential $\mu \rightarrow 0 $. But what happens if interaction is taken into account?
 A: Bose-Einstein condensation per se is a non-interacting effect, solely driven by particle statistics. In $d=2$ dimensions, free space, the energy density is such that particles can still be accommodated in the excited states for $T \neq 0$ thereby not triggering the macroscopic occupation of the ground state.
This does not mean that you cannot superfluidity (SF) in 2D. Superfluidity is not the same thing as BEC. SF just means that you have a critical velocity $v_{\mathrm{c}}$ below which the fluid experiences no dissipation. But $v_{\mathrm{c}}$ depends on the interaction strength, so if you want in 3D the BEC is a "boring SF" with $v_{\mathrm{c}} = 0$.
You can still have a mechanism that allows SF in a 2D fluid. It's called the BKT transition, and is driven by the energy favourability of creating free/bound vortices. The vortex size is determined by the interaction length (healing length of the wavefunction), so it only plays a rôle for an interacting gas. You don't consider BKT in a 3D gas because they are unstable anyway (line vortex instability).
Interesting literature: 


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*this paper, where they connected the BEC and BKT phase transitions by changing the interactions strength of a 2D/3D trapped atomic gas.

*this paper, where they look at a BEC on the surface of a sphere, where, depending on the radius of curvature, you can have BEC or BKT.
