A Coherent-State Approach to Two-dimensional Electron Magnetism

We study in this paper the possible occurrence of orbital magnetim for twodimensional electrons confined by a harmonic potential in various regimes of temperature and magnetic field. Standard coherent state families are used for calculating symbols of various involved observables like thermodynamical potential, magnetic moment, or spatial distribution of current. Their expressions are given in a closed form and the resulting Berezin-Lieb inequalities provide a straightforward way to study magnetism in various limit regimes. In particular, we predict a paramagnetic behaviour in the thermodynamical limit as well as in the quasiclassical limit under a weak field. Eventually, we obtain an exact expression for the magnetic moment which yields a full description of the phase diagram of the magnetization. PACS: 75.20.-g: diagmagnetism, paramagnetism, superparamagnetism, 75.30.Kz: magnetic phase boundary, 71.10.Ca: Electron gas, Fermi gas, 51.60: magnetic phenomena in gases