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Based on the rainbow approximation of Dyson-Schwinger equation and the assumption that the inverse dressed fermion propagator at finite chemical potential is analytic in the neighborhood of 0, A new method for calculating the dressed fermion propagator at finite chemical potential in QED 3 is developed. From this the effects of the chemical potential on the critical number of the fermion flavors is evaluated.

The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial-vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson-Schwinger equations.

Based on the study of the linear response of the fermion propagator in the presence of an external scalar field, we calculate the staggered spin susceptibility in the low energy limit in the framework of the Dyson-Schwinger approach. We analyze the effect of a finite gauge boson mass on the staggered spin susceptibility in both Nambu phase and Wigner phase. It is found that the gauge boson mass suppresses the staggered spin susceptibility in Wigner phase. In addition, we try to give an explanation for why the antiferromagnetic spin correlation increases when the doping is lowered.Comment: 7 pages, 5 figures. arXiv admin note: text overlap with arXiv:1306.301