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 $n_c=(mT/2\mathrm{}\pi {ħ}^2)\ln (\xi {ħ}^2/mU)$ and ${\mu }_c=(mTU/\pi {ħ}^2)\ln ({\xi }_{\mu }{ħ}^2/mU)$, where $T$ is the temperature, $m$ is the mass, and $U$ is the effective interaction. The dimensionless constant $\xi =380\mathrm{}\pm 3$ is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For ${\xi }_{\mu }$ our result is ${\xi }_{\mu }=13.2\mathrm{}\pm 0.4$. We also report the study of the quasicondensate correlations at the critical point.