Non-analytic dependence of the transition temperature of the homogeneous dilute Bose gas on scattering length

Markus Holzmann, Gordon Baym, Jean-Paul Blaizot, Franck Laloe

Published 2001-03-29, updated 2001-07-19Version 3

We show that the shift in the transition temperature of the dilute homogeneous Bose gas is non-analytic in the scattering amplitude, $a$. The first correction beyond the positive linear shift in $a$ is negative and of order $a^2\ln a$. This non-universal non-analytic structure indicates how the discrepancies between numerical calculations at finite $a$ can be reconciled with calculations of the limit $a \to0$, since the linearity is apparent only for anomalously small $a$.