REAL-SPACE RENORMALIZATION-GROUP INVESTIGATION OF PURE AND DISORDERED MIXED SPIN ISING-MODELS ON D-DIMENSIONAL LATTICES

The mixed spin Ising model (spins σ=1/2 and S=1) on d-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 for d=2 and d>2. For any dimension d 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 on d. 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 interactions Kij are assumed to be independent random variables with distribution P(Kij)=pδ(Kij-K)+(1-p)δ(Kij-αK); where K>0. The phase diagrams for different values of p are obtained. At zero temperature, it is found that in the bond diluted model (α=0) the value (L/K)0 depends continuously on p, whereas in the random ±K interactions (α=-1) (L/K)0 is unique and does not depend on p. © 1990 Springer-Verlag.