Non-Analytic Vertex Renormalization of a Bose Gas at Finite Temperature

We derive the flow equations for the symmetry unbroken phase of a dilute 3-dimensional Bose gas. We point out that the flow equation for the interaction contains parts which are non-analytic at the origin of the frequency-momentum space. We examine the way this non-analyticity affects the fixed point of the system of the flow equations and shifts the value of the critical exponent for the correlation length closer to the experimental result in comparison with previous work where the non-analyticity was neglected. Finally, we emphasize the purely thermal nature of this non-analytic behaviour comparing our approach to a previous work where non-analyticity was studied in the context of renormalization at zero temperature.