The spin-1 Ising spin glass: a renormalization-group approach

The nearest-neighbour-interaction spin-1 Ising spin glass, in the presence of a random crystal field, is considered on diamond hierarchical lattices o f fractal dimensions d = 2, 3 and 4. The coupling constants and crystal fie lds follow Gaussian probability distributions, which are taken as independe nt, at the beginning of the iteration process. By monitoring simultaneously the evolution of two probability distributions, associated respectively wi th the renormalized coupling constants and crystal fields, the phase diagra ms of the model are obtained. A spin-glass phase, at finite temperatures, i s found for hierarchical lattices with d = 3 and 4, but not for d = 2. Two distinct attractors characterized by zero effective coupling constants are detected. Following the usual procedure, i.e. associating an equilibrium ph ase with each basin of attraction, one obtains two phases with absence of m agnetic order, namely, a zero-spin phase (where the spins prefer the 0 stat e) and a +/-1-spin phase (where the spins prefer +/-1 states at random).