Transition Temperature of the homogeneous, weakly interacting Bose gas

TL;DR

This paper uses Monte Carlo simulations to accurately determine how small interactions affect the transition temperature of a three-dimensional Bose gas, avoiding finite-size scaling assumptions.

Contribution

It introduces a Monte Carlo method that calculates the transition temperature shift in a large, weakly interacting Bose gas without relying on finite-size scaling.

Findings

Determined the transition temperature shift for up to 20,000 bosons.

Showed the independence of results from the order of limits taken.

Provided detailed analysis of the ideal non-interacting system at finite N.

Abstract

We present a Monte Carlo calculation for up to $N \sim 20 000$ bosons in 3 D to determine the shift of the transition temperature due to small interactions $a$. We generate independent configurations of the ideal gas. At finite $N$, the superfluid density changes by a certain correlation function in the limit $a \to 0$; the $N \to \infty$ limit is taken afterwards. We argue that our result is independent of the order of limits. Detailed knowledge of the non-interacting system for finite $N$ allows us to avoid finite-size scaling assumptions.