THE FREE ENERGY OF THE TWO-DIMENSIONAL DILUTE BOSE GAS. I. LOWER BOUND

We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density and inverse temperature fi differs from the one of the noninteracting system by the correction term 4 2 jln a2 j 1.2 T1 fi c=fiU2 C/. Here, a is the scattering length of the interaction potential, TU C D max f0; g and fi c is the inverse Berezinskii-Kosterlitz-Thouless critical temperature for superfluidity. The result is valid in the dilute limit a2 1 and if fi & greater than or similar to 1.