Frustrated quantum two-dimensional J 1-J 2-J 3 antiferromagnet in a spherically symmetric self-consistent approach

In the framework of a spherically symmetric self-consistent approach to two-time retarded spin-spin Green's functions, we develop the theory of a two-dimensional frustrated J (1) -J (2) -J (3) quantum S=1/2 antiferromagnet. We show that taking the damping of spin fluctuations into account is decisive in forming both the spin-liquid state and the state with long-range order. In particular, the existence of damping allows explaining the scaling behavior of the susceptibility chi(q, omega) of the CuO (2) cuprate plane, the behavior of the spin spectrum in the two-plane case, and the occurrence of an incommensurable chi(q, omega) peak. In the case of the complete J(1)-J (2) -J (3) model, in a single analytic approach, we find continuous transitions between three phases with long-range order (checkerboard, stripe, and helical (q, q) phases) through the spin-liquid state. We obtain good agreement with cluster computations for the J (1) -J (2) -J (3) model and agreement with the neutron scattering data for the J (1) -J (2) model of cuprates.