We consider the phase transition in a ferromagnet with line defects that

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Real crystals almost unavoidably contain a finite density of dislocations. We show that this generic type of long-range correlated disorder leads to a breakdown of the conventional scenario of critical behavior and standard renormalization group techniques based on the existence of a simple, homogeneous ground state. This breakdown is due to the appearance of an inhomogeneous ground state that changes the character of the phase transition to that of a percolative phenomenon. This scenario leads to a natural explanation for the appearance of two length scales in recent high resolution small-angle scattering experiments near magnetic and structural phase transitions. 64.60.Ak,75.10.NrThe modern theory of phase transitions (PTs) in pure and weakly disordered crystals is based on the scaling hypothesis and the renormalization group (RG). It has been confirmed by a large number of experiments and numerical simulations.Therefore, the results of some recent high resolution X-ray and neutron scattering experiments for various crystals near structural and magnetic PTs were quite unexpected [1]: in contrast to the predictions of conventional scaling theory two distinct large scales were observed. The temperature dependence of the smaller scale was found to be broadly consistent with the results of the conventional theory for the correlation scale of thermal fluctuations. Quite recently explicit experimental evidence for Verneuil grown samples of SrTiO 3 [2] confirmed earlier speculations that the second, larger scale is connected with the presence of defects in a very large region near the surface.All experiments that found two length scales used crystals which were considered to be of good quality. Nevertheless, surface preparation creates a significant density of defects in a surface layer with a thickness up to several µ [1-4]. Based on this observation, Altarelli et al. suggested [5] that most of the defects are actually dislocation dipoles which induce elastic strains with a pair correlator G(r) ∼ |r| −2 . They tried to explain the critical behavior (CB) in the disordered layer as that of the Weinrib-Halperin (WH) model [6]. The coexistence of two scales was then interpreted as a simple superposition effect, with scattering from the larger scale in the disordered layer (where the CB is governed by the WH fixed point) and from the smaller scale (corresponding to conventional CB) in the bulk of the sample. However, later experiments using very thin Holmium films found clear evidence that near the magnetic PT temperature both scales coexist in the same volume fraction of the sample [7].By construction, the conventional RG procedure is not able to explain the simultaneous existence of two length scales. Not only its detailed value and temperature dependence, but even the principal theoretical basis for the origin of the second length scale appears to be unclear.In this Letter we point out the shortcomings of the RG procedure for the treatment of systems with weak, but long-range (LR) correlated disorder, the generic sit...

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