Two-dimensional gases of generalized statistics in a uniform magnetic field

TL;DR

This paper investigates the low-temperature behavior of two-dimensional gases with generalized statistics, such as parafermion and exclusion statistics, in a magnetic field, highlighting their equivalence at zero temperature and discussing implications for the quantum Hall effect.

Contribution

It introduces a comparative analysis of parafermion and exclusion statistics gases in magnetic fields, revealing their equivalence at zero temperature and exploring potential effects on the quantum Hall phenomenon.

Findings

Parafermion and exclusion statistics gases behave similarly at low temperatures.

These gases become exactly equivalent at zero temperature.

Implications for the quantum Hall effect are discussed.

Abstract

We study the low temperature properties of two-dimensional ideal gases of generalized statistics in a uniform magnetic field. The generalized statistics considered here are the parafermion statistics and the exclusion statistics. Similarity in the behaviours of the parafermion gas of finite order $p$ and the gas with exclusion coefficient $g=1/p$ at very low temperatures is noted. These two systems become exactly equivalent at $T=0$. Qumtum Hall effect with these particles as charge carriers is briefly discussed.