Abstract
The critical temperatures T c and the mean-field critical coefficients of the susceptibility χ are calculated for the S=1/2 Heisenberg-Ising model on the simple cubic lattice by the Kikuchi approximation and its simplified versions. χ shows a coherent anomaly. It means that the coherent-anomaly method (CAM) is applicable to evaluate the true critical temperature T c * and the non-classical critical exponent γ for the susceptibility. As a result, the dependence of T c * on an anisotropy parameter η is given. It is shown that the behavior of γ versus η approaches a flat line step by step as the corrections up to the higher order approximation are taken into account for 0 ≤ η < 1
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