First Order Phase Transition in a Model for Generalized Statistics

TL;DR

This paper identifies a first order phase transition in a model for generalized exclusion statistics, specifically analyzing the case of Fermi statistics, revealing different behaviors in canonical and grandcanonical ensembles.

Contribution

It characterizes the phase transition in both ensembles for the Fermi exclusion case, highlighting ensemble-dependent features such as latent heat and energy discontinuity.

Findings

No latent heat in grandcanonical ensemble

Finite jump in particle number in grandcanonical ensemble

Discontinuous internal energy in canonical ensemble

Abstract

A first order phase transition is found in a model which was introduced originally by Murthy and Shankar [Phys. Rev. B 60, 6517 (1999)] to describe systems of generalised exclusion statistics. I characterise the phase transition in the canonical and grandcanonical ensebles for the case when the statistical exclusion parameter is 1, which corresponds to the Fermi exclusion statistics. We observe that in the grandcanonical ensemble the phase transition has no latent heat, but it has a finite jump in the particle number. In canonical conditions--when the particle number is held fix--the internal energy is discontinuous at the transition.