Second-order phase transition in crystals with long-range correlated quenched defects

We consider the phase transition in a ferromagnet with line defects that introduce a local variation of the critical temperature V(r)∝${\mathit{r}}_{\mathrm{\perp }}^{\mathrm{-}\mathrm{\Delta }}$, leading to a correlator 〈V(0)V(r)〉∝${\mathit{r}}_{\mathrm{\perp }}^{\mathrm{-}\left(2\mathrm{}\mathrm{\Delta }\mathrm{-}\mathit{d}\right)}$. We discuss conditions of both local and global character that lead to different scenarios for the transition, ranging from a ‘‘conventional’’ transition into a homogeneous phase that can be described within the framework of the standard renormalization group to a transition into an inhomogeneous phase with a percolating network of ordered regions. © 1996 The American Physical Society.