Real-space renormalization group investigation of pure and disordered mixed spin Ising models ond-dimensional lattices

The mixed spin Ising model (spins =1/2 andS=1) ond-dimensional hypercubic lattices with nearest-neighbour exchange interactions is studied via a renormalization group transformation in position space. The phase diagrams in (L, K) space, i.e. in dependence of the bilinear (K) and the biquadratic (L) interaction coefficients, are qualitatively different ford=2 andd>2. For any dimensiond however it is found that all transitions are of second order. At zero-temperature (K=,L=), the ferromagnetic order disappears at (L/K)₀=2, which does not depend ond. Using an extension of this real-space renormalization group analysis we study the two-dimensional random disordered version of the above model.L is kept homogeneous and the bilinear interactionsK _ij are assumed to be independent random variables with distributionP(K _ij )=p(K _ij –K)+(1–p)(K _ij –K); whereK>0. The phase diagrams for different values ofp are obtained. At zero temperature, it is found that in the bond diluted model (=0) the value (L/K)₀ depends continuously onp, whereas in the random ±K interactions (=–1) (L/K)₀ is unique and does not depend onp.Supported by the agreement of cooperation between the DFGW. Germany and the CNR-Maroc