Tc for homogeneous dilute Bose gases: a second-order result
Abstract
The transition temperature for a dilute, homogeneous, three-dimensional Bose gas has the expansion Tc = T0 1 + c1 a n(1/3) + [c2' ln(a n(1/3)) + c2''] a2 n(2/3) + O(a3 n), where a is the scattering length, n the number density, and T0 the ideal gas result. The first-order coefficient c1 depends on non-perturbative physics. In this paper, we show that the coefficient c2' can be computed perturbatively. We also show that the remaining second-order coefficient c2'' depends on non-perturbative physics but can be related, by a perturbative calculation, to quantities that have previously been measured using lattice simulations of three-dimensional O(2) scalar field theory. Making use of those simulation results, we find Tc = T0 1 + (1.32+-0.02) a n(1/3) + [19.7518 ln(a n(1/3)) + (75.7+-0.4)] a2 n(2/3) + O(a3 n).
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