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Physica A Statistical Mechanics and its Applications

Renormalization group approach to the interacting bose fluid

F.W. Wiegel

Published Apr 1, 1978• 16 citations
Publisher
DOI
10.1016/0378-4371(78)90064-x

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A nonlinear analysis of differential renormalization-group (RG) equations for the interacting Bose fluid is carried out to O(\ensuremath{\epsilon}) for T=0 and in the limit n\ensuremath{\rightarrow}\ensuremath{\infty} for finite T. The 1/n expansion is shown to provide a more convenient framework than the \ensuremath{\epsilon} expansion for deriving global RG solutions that match onto the classical (T\ensuremath{\rightarrow}\ensuremath{\infty}) and quantum (T\ensuremath{\rightarrow}0) limits and which incorporate the interplay between classical and quantum fluctuations.
We derive an approximate closed form for the infinitesimal generator of the renormalization group for the interacting Bose fluid. The Bose-condensed phase is treated by the method of Bogoliubov, and a simple scaling law is found for the condensate density. It is shown that the quantum-mechanical features are irrelevant close to the $\ensuremath{\lambda}$ line. This is demonstrated by calculating the critical behavior in $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions to order $\ensuremath{\epsilon}$.