Critical properties of the mixed Ising ferromagnet

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Abstract
A real-space rescaling method is applied to the mixed, spin-1/2, Ising ferromagnet. Both bond and site disorder are considered where, respectively, bonds JA, JB or sites A, B occur with probabilities p, 1-p. For the bond-disordered case, critical curves are obtained for the square lattice for a range of alpha identical to JB/JA. Slopes at p=0,1 are in very good agreement with exact results previously obtained and Tc(p-1/2) agrees to within a few per cent with an exact result obtained by Fisch. For the more realistic site-disordered problem only the case where bond strengths are related by tanh JAAtanh JBB=tanh2 JAB is considered. Critical curves are plotted for various alpha for the square and triangular lattices. The results agree well with exact limiting slopes available for the square lattice. Thermal, percolation and crossover exponents are also calculated for both the site- and bond-disordered cases.