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

TL;DR

This study investigates the thermodynamic behavior of the noncommutative quantum Hall effect with anomalous magnetic moment, revealing how parameters influence free energy, entropy, and energy in relativistic and nonrelativistic regimes.

Contribution

It provides explicit calculations of thermodynamic properties in noncommutative quantum Hall systems with AMM, highlighting the effects of NC parameters and magnetic fields.

Findings

Helmholtz free energy decreases with temperature

Entropy increases with temperature

Mean energy and heat capacity are proportional to temperature and differ between relativistic and nonrelativistic cases

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 in the high temperatures regime. Thus, we use the canonical ensemble for a set of $N$-particles in contact with a thermal bath. Next, we explicitly determine the thermodynamic properties of our interest, namely: the Helmholtz free energy, the entropy, the mean energy, and the heat capacity. In order to perform the calculations, we work with the Euler-MacLaurin formula to construct the partition function of the system. In that way, we plotted the graphs of thermodynamic properties as a function of temperature for six different values of the magnetic field and of the NC parameters. As a result, we note that the Helmholtz free energy decreases with the temperature, increases with the NC parameters, and can decrease or increase for certain values of the magnetic field, white that the entropy increases with the temperature, decreases with the NC parameters, and can decrease or increase for certain values of the magnetic field. Besides, the mean energy increases linearly with the temperature and its values for the relativistic case are twice of the nonrelativistic case, consequently, the heat capacity for the relativistic case is twice of the nonrelativistic case, where both are constants, and therefore, satisfying the so-called Dulong-Petit law. Finally, we also verify that there is no influence of the AMM on the thermodynamic properties of the system.