Geodesic
THE FREE ENERGY OF THE TWO-DIMENSIONAL DILUTE BOSE GAS. I. LOWER BOUND
Forum of Mathematics, Sigma, Tome 8 (2020)

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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 $\unicode[STIX]{x1D70C}$ and inverse temperature $\unicode[STIX]{x1D6FD}$ differs from the one of the noninteracting system by the correction term $4\unicode[STIX]{x1D70B}\unicode[STIX]{x1D70C}^{2}|\ln \,a^{2}\unicode[STIX]{x1D70C}|^{-1}(2-[1-\unicode[STIX]{x1D6FD}_{\text{c}}/\unicode[STIX]{x1D6FD}]_{+}^{2})$. Here, $a$ is the scattering length of the interaction potential, $[\cdot ]_{+}=\max \{0,\cdot \}$ and $\unicode[STIX]{x1D6FD}_{\text{c}}$ is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit $a^{2}\unicode[STIX]{x1D70C}\ll 1$ and if $\unicode[STIX]{x1D6FD}\unicode[STIX]{x1D70C}\gtrsim 1$. 
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     author = {ANDREAS DEUCHERT and SIMON MAYER and ROBERT SEIRINGER},
     title = {THE {FREE} {ENERGY} {OF} {THE} {TWO-DIMENSIONAL} {DILUTE} {BOSE} {GAS.} {I.} {LOWER} {BOUND}},
     journal = {Forum of Mathematics, Sigma},
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ANDREAS DEUCHERT; SIMON MAYER; ROBERT SEIRINGER. THE FREE ENERGY OF THE TWO-DIMENSIONAL DILUTE BOSE GAS. I. LOWER BOUND. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.17

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