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利用三维量子电动力学理论中的Dyson-Schwinger方程方法,研究了零温情况下平面铜氧化合物超导体的反铁磁相和d波超导相之间的相变．通过在朗道规范下近似解析求解和数值求解完全耦合的Dyson-Schwinger方程、并将所得结果与1/N展开方法的结果相比较,发现在半填充准费密子味道数约小于等于4的情况下,通过手征对称性自发破缺,d波超导相可以演化到反铁磁相,并且反铁磁相有可能与d波超导相共存．通过进一步比较不同相的压强,还说明反铁磁与d波超导共存相为稳定相,从而反铁磁相确实可以与d波超导相共存．
The Dyson-Schwinger equation method in three-dimensional quantum electrodynamics is used to study the phase transition between the antiferromagnetic and d-wave superconducting phases in planar copper oxide superconductors at zero temperature. By the approximate analytic solution and the numerical solution of the perfectly coupled Dyson-Schwinger equation under Landau’s rule, and comparing the results with those of the 1 / N expansion method, it is found that when the half-filled quasi-confit mass taste is less than or equal to 4 In this case, the d-wave superconducting phase can evolve to the anti-ferromagnetic phase by spontaneous breaking of the chiral symmetry, and the anti-ferromagnetic phase may co-exist with the d-wave superconducting phase. By further comparing the pressure of different phases, it is also shown that the coexisting phases of antiferromagnetic and d-wave superconductors are stable phases, so that the antiferromagnetic phase can indeed co-exist with the d-wave superconducting phase.