Orbital magnetism in two-dimensional integrable systems

We study orbital magnetism of a degenerate electron gas in a number of two-dimensional integrable systems, within linear response theory. There are three relevant energy scales: typical level spacing Delta, the energy Gamma, related to the inverse time of flight across the system, and the Fermi energy epsilon(F). Correspondingly, there are three distinct temperature regimes: microscopic (T much less than Delta), mesoscopic (Delta much less than T less than or similar to Gamma) and macroscopic (Gamma much less than T much less than epsilon(F)) In the first two regimes there are large finite-size effects in the magnetic susceptibility chi, whereas in the third regime chi approaches its macroscopic value. In some cases, such as a quasi-one-dimension al strip or a harmonic confining potential, it is possible to obtain analytic expressions for chi in the entire temperature range.