The critical behavior of the spin-1 Ising model with a bimodal random crystal field: Renormalization group study

Abstract

Phase diagrams of the spin-1 Ising model with a random crystal field Δ on a two- and three-dimensional lattice were investigated using renormalization group theory. The random crystal field is distributed according to the general two pics law P(Δi)=pδ(Δi−(1−α)Δ)+(1−p)δ(Δi−(1+α)Δ). A number of characteristic phenomena are obtained when p=0.5, such as the α-dependence of the tricritical point owing to the disorder of the crystal field. When α≥0.7 for d=2 and α≥0.93 for d=3, the first-order transition is destroyed for all values of the crystal field Δ. We also found that, in the d=3 case and under certain conditions of α, the system may exhibit a reentrant behavior. A comparison with recent works on the Blume–Capel model with random crystal field is discussed.