Thermodynamic properties of the noncommutative quantum Hall effect with anomalous magnetic moment

Abstract

In this paper, we study the thermodynamic properties of the noncommutative quantum Hall effect (NCQHE) with anomalous magnetic moment (AMM) for both relativistic and nonrelativistic cases at high temperatures, where the thermodynamic properties are: the Helmholtz free energy, the entropy, the mean energy, and the heat capacity. We also work with the Euler-MacLaurin formula to construct the partition function. Next, we plotted the graphs of properties as a function of temperature for different values of the magnetic field and of the NC parameters. We note that the Helmholtz free energy decreases with the temperature, increases with the NC parameters, and can decrease or increase with the magnetic field, while the entropy increases with the temperature, decreases with the NC parameters, and can decrease or increase with the magnetic field. Besides, the mean energy increases linearly with the temperature and the heat capacity satisfies the Dulong-Petit law, which also verified that the AMM does not influence the thermodynamic properties.