Transition Temperature for Weakly Interacting Homogeneous Bose Gases

Abstract

We apply the non-perturbative optimized linear $\delta$ expansion method to the O(N) scalar field model in three-dimensions to determine the transition temperature of a dilute homogeneous Bose gas. Our results show that the shift of the transition temperature, $\Delta T_c/T_c$, of the interacting model, compared with the ideal gas transition temperature, really behaves as $\gamma a{n}^{1/3}$ where $a$ is the s-wave scattering length and $n$ is the number density. For $N=2$ our calculations yield the value $\gamma =3.059$.

9 pages, REVTEX. New sections added, revised and extended text, new refs

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