Instabilities in Ising systems with short- and long-range-correlated quenched random fields

The ferromagnetically ordered states of Ising systems with short-range-correlated random fields are shown to be unstable with respect to domain formation for dimensionalities d<or=d l =2. Domain wall roughening for 2<d<5 follows from the same mechanism as the Imry and Ma (1975) domain formation for d<or=2. No additional instabilities for d>or=2 are found. The results are extended to random fields with a correlation function obeying a power law approximately r -a for large separation r. For a>d the same results as for short-range field correlations are found. For a<d the author finds domain formation for a<or=a l =2 and wall roughening for a<or=4 (d>or=5) and a<d(d<5). The borderline value for a above which the mean-field theory is valid is found to be six. Experimental consequences of these results are indicated.