Second Order Phase Transition in Crystals with Long--Range Correlated Quenched Defects

Abstract

We consider the phase transition in a ferromagnet with line defects that introduce a local variation of the critical temperature V (r) / r \Gamma\Delta ? , leading to a correlator hV (0)V (r)i / r \Gamma(2\Delta\Gammad) ? . 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. 64.60Ak Typeset using REVT E X I. INTRODUCTION There have been many investigations of the thermodynamic properties of crystals with quenched defects of the random temperature type near a second order phase transition point. 1 These defects can be described by an additional term H def = X k V d (r \Gamma r k )\Theta(r k ) j'(r)j 2 j V (r)j'(r)j 2 (1) in the Hamiltonian density. Here V d (r \Gamma r k ) is a si..