Two-dimensional weakly interacting Bose gas in the fluctuation region

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 quasicondensate 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.