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Title: Shift of the condensation temperature caused by weak repulsion
Plain: Weak repulsion between bosons raises their condensation temperature slightly, in proportion to the interaction strength. The coefficient is known only from computer simulations.
Precise: For the dilute 3D Bose gas, prove that $(T_{c} - T_{c}^{0})/T_{c}^{0} = c\rho^{1/3}a + o(\rho^{1/3}a)$, with $T_{c}^{0}$ the ideal-gas value, and determine c (lattice Monte Carlo gives c approximately 1.3, Arnold and Moore; Kashurnikov, Prokof'ev and Svistunov, 2001). Answer: the existence of the phase transition and the value of c.
Settled by: A proof of a phase transition at $T_{c}$ with rigorous bounds on $c$.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: (empty)
Posed since: (empty)