Critical exponents and fluctuations at BEC in a 2D harmonically trapped ideal gas

TL;DR

This paper investigates the critical behavior and fluctuations of a 2D ideal Bose gas in a harmonic trap, revealing universal critical exponents and the nature of the phase transition through exact numerical analysis.

Contribution

It provides an exact numerical characterization of the critical properties and fluctuations of a 2D trapped ideal Bose gas, including correlation length and critical exponents.

Findings

Correlation length diverges at critical temperature

Logarithmic singularities linked to thermodynamic non-analyticity

Critical exponents define a unique universality class

Abstract

The critical properties displayed by an ideal 2D Bose gas trapped in a harmonic potential are determined and characterized in an exact numerical fashion. Beyond thermodynamics, addressed in terms of the global pressure and volume which are the appropriate variables of a fluid confined in a non-uniform harmonic potential, the density-density correlation function is also calculated and the corresponding correlation length is found. Evaluation of all these quantities as Bose-Einstein condensation (BEC) is approached manifest its critical continuous phase transition character. The divergence of the correlation length as the critical temperature is reached, unveils the expected spatial scale invariance proper of a critical transition. The logarithmic singularities of this transition are traced back to the non-analytic behavior of the thermodynamic variables at vanishing chemical potential, which is the onset of BEC. The critical exponents associated with the ideal BEC transition in the 2D inhomogeneous fluid reveals its own universality class.