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We study the stability of the highest symmetric solution (Wigner-solution) ofDyson-Schwinger equations in chiral limit and at zero temperature. Our resultsconfirm that if the chemical potential is not very large, the QCD vacuum is inthe chiral symmetry breaking phase and the quantum phase-transition of thechiral symmetry restoration is in first order. Meanwhile it seems that there isnot competition between chiral symmetry breaking phase and colorsuperconductivity phase since the color superconductivity phase appears only ifthe chemical potential is very large. Moreover, we propose that chiral symmetrybreaking arises from the positive feedback with respect to the massperturbation.

Dyson-Schwinger Equation and Quantum Phase Transitions in Massless QCD