  We investigate the general features of the renormalization-group flow at the
Berezinskii-Kosterlitz-Thouless (BKT) transition, providing a thorough
quantitative description of the asymptotc critical behavior, including the
multiplicative and subleading logarithmic corrections. For this purpose, we
consider the RG flow of the sine-Gordon model around the renormalizable point
which describes the BKT transition. We reduce the corresponding beta-functions
to a universal canonical form, valid to all perturbative orders. Then, we
determine the asymptotic solutions of the RG equations in various critical
regimes: the infinite-volume critical behavior in the disordered phase, the
finite-size scaling limit for homogeneous systems of finite size, and the
trap-size scaling limit occurring in 2D bosonic particle systems trapped by an
external space-dependent potential.
