Pollet, LProkof'ev, NikolaiSvistunov, Boris2024-04-262024-04-262010-01-01https://hdl.handle.net/20.500.14394/40587This is the pre-published version harvested from ArXiv. The published version is located at http://prl.aps.org/abstract/PRL/v104/i24/e245705We discuss generic limits posed by the trap in atomic systems on the accurate determination of critical parameters for second-order phase transitions, from which we deduce optimal protocols to extract them. We show that under current experimental conditions the in situ density profiles are barely suitable for an accurate study of critical points in the strongly correlated regime. Contrary to recent claims, the proper analysis of time-of-fight images yields critical parameters accurately.Physical Sciences and MathematicsPhysicsarticle