High-temperature series expansion of the spin correlation functions on the B-spinel lattice are computed to order 6 in for Heisenberg model having both nearest- and next-nearest-neighbour exchange integrals. The results are given for various neighbour correlations (up to the third). The behaviour with the temperature and the site dilution is presented. The obtained results provide a useful tool for a straightforward interpretation and understanding of experimental data. The approach is applied to the experimental results of the B-spinel in the dilution range . The critical temperature and the critical exponents for the susceptibility and the correlation length are deduced by applying the Padé approximant methods. The following estimates are obtained for the familiar critical exponents: and . These values are not sensitive to the dilution ratio x. The transition temperatures as a function of x obtained by the present theory are found to be in excellent agreement with the experimental ones.

The critical properties of a ferrimagnetic spinel system (AB 2 X 4 , A and B are magnetic ions) are studied by the method of exact high-temperature series expansions. Terms up to seventh order were computed for the magnetic susceptibility χ = 7 n=0 a n ( 1 k B T ) n . The calculations are given for the three nearest neighbours' exchange integrals J AA , J AB and J BB . The Padé approximants method is used to estimate the critical exponent γ associated with the magnetic susceptibility. A net variation of γ with exchange couplings has been observed. This variation presents some unusual characteristics. The magnetic asymmetric interactions and the competition between the exchange interactions are important for the magnetic phase transition in ferrimagnetic spinels.We make comparisons with experiment by studying real Heisenberg spinel ferrite systems ACr 2 S 4 (A = Fe, Co). The results of γ and T c obtained by the present approach are in agreement with the experimental values.

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