article published yes Andreas Deuchert author 4DA65CD0-F248-11E8-B48F-1D18A9856A870000-0003-3146-6746 Simon Mayer author 30C4630A-F248-11E8-B48F-1D18A9856A87 Robert Seiringer author 4AFD0470-F248-11E8-B48F-1D18A9856A870000-0002-6781-0521 RoSe department Analysis of quantum many-body systems project 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 𝜌 and inverse temperature 𝛽 differs from the one of the noninteracting system by the correction term 𝜋𝜌𝜌𝛽𝛽 . Here, is the scattering length of the interaction potential, and 𝛽 is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit 𝜌 and if 𝛽𝜌 . https://research-explorer.ista.ac.at/download/7790/7797/2020_ForumMath_Deuchert.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Cambridge University Press2020 eng 20505094 1910.03372 00052734200000110.1017/fms.2020.17 8 https://research-explorer.ista.ac.at/record/7524 Deuchert A, Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 8, e20. Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2020. <a href="https://doi.org/10.1017/fms.2020.17">https://doi.org/10.1017/fms.2020.17</a>. A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020). Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 8, e20, Cambridge University Press, 2020, doi:<a href="https://doi.org/10.1017/fms.2020.17">10.1017/fms.2020.17</a>. Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. 2020;8. doi:<a href="https://doi.org/10.1017/fms.2020.17">10.1017/fms.2020.17</a> Deuchert, A., Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href="https://doi.org/10.1017/fms.2020.17">https://doi.org/10.1017/fms.2020.17</a> A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 8. Cambridge University Press, 2020. 77902020-05-03T22:00:48Z2025-06-26T09:44:52Z