The effects of quenched dipole moments on a two-dimensional Heisenberg antiferromagnet are found exactly, by applying the renormalization group to the appropriate classical non-linear sigma model. Such dipole moments represent random fields with power law correlations. At low temperatures, they also represent the long range effects of quenched random strong ferromagnetic bonds on the antiferromagnetic correlation length, ξ2D, of a two-dimensional Heisenberg antiferromagnet. It is found that the antiferromagnetic long range order is destroyed for any non-zero concentration, x, of the dipolar defects, even at zero temperature. Below a line T ∞ x, where T is the temperature, ξ2D is independent of T, and decreases exponentially with x. At higher temperatures, it decays exponentially with ρeffs/T, with an effective stiffness constant ρeffs, which decreases with increasing x/T. The latter behavior is the same as for annealed dipole moments, and we use our quenched results to interpolate between the two types of averaging for the problem of ferromagnetic bonds in an antiferromagnet. The results are used to estimate the three-dimensional Néel temperature of a lamellar system with weakly coupled planes, which decays linearly with x at small concentrations, and drops precipitously at a critical concentration. These predictions are shown to reproduce successfully several of the prominent features of experiments on slightly doped copper oxides.
- 75.10.-b General theory and models of magnetic ordering
- 75.10.Nr Spin-glass and other random models
- 75.50.Ee Antiferromagnetics