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In the framework of the O(N) three-dimensional effective scalar field modelfor homogeneous dilute weakly interacting Bose gases we use the 1/N expansionto evaluate, within the large N limit, the parameter r_c which is directlyrelated to the critical chemical potential mu_c. This quantity enters theorder-a^2 n^{2/3} coefficient contributing to the critical temperature shiftDelta T_c where a represents the s-wave scattering length and n represents thedensity. Compared to the recent precise numerical lattice simulation results,our calculation suggests that the large N approximation performs rather welleven for the physical case N=2. We then calculate the same quantity but usingdifferent forms of the optimized perturbative (variational) method, showingthat these produce excellent results both for the finite N and large-N cases.Comment: 12 pages, 2 figures. We have performed a refined and extended  numerical analysis to take into account the very recent results of Ref. [15

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Exact<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math>and optimized perturbative evaluation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>μ</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math>for homogeneous interacting Bose gases

Exact1∕Nand optimized perturbative evaluation ofμcfor homogeneous interacting Bose gases