Universal thermodynamics of a two-dimensional Bose gas

Using renormalization-group arguments we show that the low-temperature thermodynamics of a three-or two-dimensional dilute Bose gas is fully determined by a universal scaling function F-d(mu/k(B)T, (g) over tilde (T)) once the mass m and the s-wave scattering length a(d) of the bosons are known (d is the space dimension). Here mu and T denote the chemical potential and temperature of the gas, and the temperature-dependent dimensionless interaction constant (g) over tilde (T) is a function of ma(d)(2)k(B)T/(h) over bar (2). We compute the scaling function F-2 using a nonperturbative renormalization-group approach and find that both the mu/k(B)T and (g) over tilde (T) dependencies are in very good agreement with recent experimental data obtained for a quasi-two-dimensional Bose gas with or without optical lattice. We also show that the nonperturbative renormalization-group estimate of the Berezinskii-Kosterlitz-Thouless transition temperature compares well with the result obtained from a quantum Monte Carlo simulation of an effective classical field theory.