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 absolute value psi(4) model on a lattice. The critical density and chemical potential are given by relations n(c) = (mT/2piPlanck's(2))ln(xiPlanck's(2)/mU) and mu(c) = (mTU/piPlanck's(2))ln(xi(mu)Planck's(2)/mU), where T...