2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132036We apply the Projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature $T_c$ of a harmonically confined Bose gas as reported in Gerbier \emph{et al.} [Phys. Rev. Lett. \textbf{92}, 030405 (2004)]. The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data. To unequivocally observe beyond mean-field effects, however, the experimental precision must either improve by an order of magnitude, or consider more strongly interacting systems. This is the first application of a classical field method to make quantitative comparison with experiment.revtex4, four pages, three figures. v2: updated to published version. Several additions to figures, and better explanations in text in response to referee commentsOther Condensed Mattertext