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.