Application of Renormalization Group Techniques to a Homogeneous Bose Gas at Finite Temperature

TL;DR

This paper applies renormalization group methods to study a homogeneous Bose gas at finite temperature, revealing a second order phase transition and calculating the critical exponent.

Contribution

It introduces a non-perturbative flow equation approach with sharp and smooth cutoffs for analyzing Bose gases at finite temperature.

Findings

System undergoes a second order phase transition

Critical exponent ν = 0.73 obtained

Method confirms universality class predictions

Abstract

A homogeneous Bose gas is investigated at finite temperature using renormalization group techniques. A non--perturbative flow equation for the effective potential is derived using sharp and smooth cutoff functions. Numerical solutions of these equations show that the system undergoes a second order phase transition in accordance with universality arguments. We obtain the critical exponent $\nu =0.73$ to leading order in the derivative expansion.