  The Beresinskii-Kosterlitz-Thouless (BKT) physics of vortices in
two-dimensional superconductors at finite magnetic field is investigated by
means of a field-theoretical approach based on the sine-Gordon model. This
description leads to a straightforward definition of the field-induced
magnetization and shows that the persistence of non-linear effects at low
fields above the transition is a typical signature of the fast divergence of
the correlation length within the BKT theory.
