Existence of a critical point in the phase diagram of the ideal relativistic neutral Bose gas

TL;DR

This paper demonstrates the existence of a critical point in the phase diagram of the ideal relativistic neutral Bose gas, revealing phase transition behaviors and confirming the Widom line in the supercritical region.

Contribution

It provides the first exact numerical analysis showing a critical point and phase transition in the relativistic Bose gas without relying on thermodynamic limit assumptions.

Findings

Critical particle number is 7616 for phase transition.

Phase transition is first-order below critical pressure, second-order at critical pressure.

Confirmed the Widom line in the supercritical region.

Abstract

We explore the phase transitions of the ideal relativistic neutral Bose gas confined in a cubic box, without assuming the thermodynamic limit nor continuous approximation. While the corresponding non-relativistic canonical partition function is essentially a one-variable function depending on a particular combination of temperature and volume, the relativistic canonical partition function is genuinely a two-variable function of them. Based on an exact expression of the canonical partition function, we performed numerical computations for up to hundred thousand particles. We report that if the number of particles is equal to or greater than a critical value, which amounts to 7616, the ideal relativistic neutral Bose gas features a spinodal curve with a critical point. This enables us to depict the phase diagram of the ideal Bose gas. The consequent phase transition is first-order below the critical pressure or second-order at the critical pressure. The exponents corresponding to the singularities are 1/2 and 2/3 respectively. We also verify the recently observed `Widom line' in the supercritical region.