Critical point of a weakly interacting two-dimensional Bose gas

We. study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical \psi\(4) model on a lattice. The critical density and chemical potential are given by relations n(c) = (mT/2 pi (h) over bar (2))ln(xi(h) over bar (2)/mU) and mu (c) = (mTU/pi(h) over bar (2))ln(xi (mu)(h) over bar (2)/mU), where T is the temperature, m is the mass, and U is the effective interaction. The dimensionless constant xi = 380 +/- 3 is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For xi (mu) our result is xi (mu) = 13.2 +/- 0.4. We also report the study of the quasicondensate correlations at the critical point.