Pure and diluted anisotropic quantum Heisenberg model

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Abstract
Pure and diluted anisotropic quantum Heisenberg models are treated by renormalisation group scaling methods. Detailed discussions are given of the dependence of transition temperature on anisotropy and concentration, and of the dependence of correlation length on anisotropy, concentration and temperature. Particular emphasis is given to the weakly anisotropic system near the percolation limit and to the weakly anisotropic and Ising-like situations near the pure limit. One-, two- and three-dimensional cases are treated in turn. Some comparisons are made with neutron scattering results for the correlation length of quasi one- and two-dimensional systems and with the measured transition temperature curve for a diluted anisotropic layer system.