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 J (1)-J (2) Heisenberg model on a two-dimensional square lattice is considered for two-time retarded spin-spin Green's functions. The spin excitation spectrum, omega(q), and spin gaps at symmetric points are obtained for the entire J (1)-J (2) diagram, i.e., for any I center dot, J (1) = cosI center dot, and J (2) = sinI center dot. The structure factor c (q) and the correlation length xi 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 a (c) 1/2 I center dot a (c) 1/2 pi), and the lower, nonfrustrated (pi a (c) 1/2 I center dot a (c) 1/2 2 pi), 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 (J (1) > J (2) > 0), the results obtained are compared with the experimental dependence of xi on temperature and doping level. A correspondence rule is proposed between frustration in a spin model and the doping of an antiferromagnet with holes.