On the existence of condensed phases in low-dimensional systems

It is shown that the threshold interaction constant (TIC) α_D for the existence of a condensed phase increases with the dimension D of a Bose system (α₃ < α₂ < α₁). TICs are evaluated exactly for a wide class of two-parameter potentials (the latter may approximate real physical interactions). The results are applied to spin-polarized systems. The possibility of an electric field induced liquid-gas transition is discussed. The TIC for N-particle clusters diminishes with N.