Spin–spin correlation length in a two-dimensional frustrated magnet and its relation to doping

In a spherically symmetric self-consistent approach (SSSA), the spin-1/2 J₁–J₂ Heisenberg model on a two-dimensional square lattice is considered for two-time retarded spin–spin Green's functions. The spin excitation spectrum, ω(q), and spin gaps at symmetric points are obtained for the entire J₁–J₂ diagram, i.e., for any ϕ, J₁ = cosϕ, and J₂ = sinϕ. The structure factor c_q and the correlation length ξ at finite temperature are calculated in the entire range of parameters. A radical difference in the behavior of the system in the upper, frustrated (0 ⩽ ϕ ⩽ π), and the lower, nonfrustrated (π ⩽ ϕ ⩽ 2π), regions of the diagram is demonstrated. In the latter region, there is a first-order phase transition that is unique on the phase diagram. For a weakly frustrated antiferromagnet (J₁ > J₂ > 0), the results obtained are compared with the experimental dependence of ξ on temperature and doping level. A correspondence rule is proposed between frustration in a spin model and the doping of an antiferromagnet with holes