Magnetic susceptibility at zero and nonzero chemical potential in QCD and QED

Abstract

Magnetic susceptibility of the quark and electron gas is calculated in a closed form for any chemical potential μ summing the whole Matsubara series. For the quark gas and small μ≪T a strong rise with T is found due to Polyakov loop factors L(T), in good agreement with lattice data. For the electron gas the lowest Matsubara term (n = 1) contributes 40% larger than the exact answer. In the case of small T, [Formula: see text], the oscillations as functions of eB occur, characteristic of the de Haas–van Alphen effect. Results are compared with available lattice data and with the case of relativistic electron gas, which obtains putting L(T)≡1.