Instability of the ferromagnetic phase under random fields in an Ising spin glass with correlated disorder

It is well established that the ferromagnetic phase remains stable under random magnetic fields in three and higher dimensions for the ferromagnetic Ising model and the Edwards-Anderson model of spin glasses without correlation in the disorder variables. In this study, we investigate an Ising spin glass with correlated disorder and demonstrate that the ferromagnetic phase becomes unstable under random fields in any dimension, provided that magnetic field chaos exists in the Edwards-Anderson model on the same lattice. Additionally, we show that this instability can also be attributed to disorder (bond) chaos. We further argue that the model with correlated disorder remains in the ferromagnetic phase even in the presence of symmetry-breaking fields, as long as the Edwards-Anderson model on the same lattice exhibits a spin glass phase under a magnetic field. These results underscore the profound impact of spatial correlations in the disorder.