Two-Dimensional Weakly Interacting Bose Gas in the Fluctuation Region

TL;DR

This paper investigates the crossover behavior of a two-dimensional weakly interacting Bose gas near the Berezinskii--Kosterlitz--Thouless transition, revealing universal relations validated by Monte Carlo simulations and mean-field theory.

Contribution

It establishes universal thermodynamic relations for the crossover region of the 2D Bose gas near the BKT transition, supported by high-precision simulations and analytic checks.

Findings

Universal relations between thermodynamic parameters are confirmed.

Monte Carlo simulations agree with mean-field analytic expressions.

The crossover behavior is characterized across the fluctuation region.

Abstract

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 quasi-condensate 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.