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We propose a new approach which permits us to obtain exact results for the mixed spin-1/2 and Spin-S (S>1/2) Ising models with single ion anisotropy Δ on the square lattice. We drive an explicit expression for the critical temperature for arbitrary values of S. We determine the exact phase diagrams for different values of S, and we show that there is no tricritical point. For S integer, there is no long range order when the anisotropy exceeds a critical value which is independent of S. Furthermore, the exact Ising transition temperature T C is always recovered, for any values of S, in the limit of Δ→−∞. These exact results are based on a conjecture which extend the analyticity of the n-spin-1/2 correlations functions (except at T=T C (Ising)) for any finite number n, to n→∞. This is confirmed by our calculations since our results are practically similar to those obtained by Monte Carlo simulations for S=1, 2 and 3/2.

Using the effective field theory with correlations, we study mixed spin4 and spin-: Ising models with random bonds and crystal-field interactions on the honeycomb lattice. The nearestneighbour couplings J,, are taken as random variables with distribution P(J,j) = p6(Ji, -J)+(1 -p)6(Jiid), where J > 0 and (a( 5 1. In a certain range of negative values of a, the phase diagrams exhibit re-entrant behaviour. In detail, we investigate separately two kinds of disorder:bond dilution (a = 0) and random fJ interactions (a = -1). In both cases, the influence of the anisotropy on the phase diagrams shows some new outstanding features.