  We study the crossover between the mean-field and critical behavior of the
two-dimensional Bose gas throughout the fluctuation region of the
Berezinskii--Kosterlitz--Thouless phase transition point. We argue that this
crossover is described by universal (for all weakly interacting |psi|^4 models)
relations between thermodynamic parameters of the system, including superfluid
and quasi-condensate densities. We establish these relations with
high-precision Monte Carlo simulations of the classical |psi|^4 model on a
lattice, and check their asymptotic forms against analytic expressions derived
on the basis of the mean-field theory.
