The influence of quenched disorder on the competition between ordered states separated by a first-order transition is investigated. A phase diagram with features resembling quantum-critical behavior is observed, even using classical models. The low-temperature paramagnetic regime consists of coexisting ordered clusters, with randomnly oriented order parameters. Extended to manganites, this state is argued to have a colossal magnetoresistance effect. A scale T * for cluster formation is discussed. This is the analog of the Griffiths temperature, but for the case of two competing orders, producing a strong susceptibility to external fields. Cuprates may have similar features, compatible with the large proximity effect of the very underdoped regime.PACS numbers: 75.30.Kz Complex phenomena such as "colossal" magnetoresistance (CMR) in manganites and high temperature superconductivity (HTS) in cuprates have challenged our understanding of correlated electrons [1]. Recent developments unveiled a previously mostly ignored aspect of doped transition-metal-oxides (TMO): these systems are intrinsically inhomogeneous, even in the best crystals. (i) The evidence in the CMR context is overwhelming. Experiments and theory provide a picture where competing ferromagnetic (FM) and charge-ordered (CO) states form microscopic and/or mesoscopic coexisting clusters [2,3]. Exciting recent experiments [4] identified features referred to as a "quantum critical point" (QCP) [5] -defined as the drastic reduction of ordering temperatures near the zero temperature (T=0) transition between ordered states -by modifying the A-site cation mean-radius r A by chemical substitution at fixed hole density (left inset of Fig. 1). The paramagnetic state in the QCP region -where the Curie temperature T C is the lowest -is crucial to understand CMR phenomenology, producing the largest CMR ratio [1,2,3]. (ii) In the HTS context, scanning tunneling microscopy (STM) studies of superconducting (SC) Bi2212 revealed a complex surface with nm-size coexisting clusters [6]. Underdoped cuprates also appear to be inhomogeneous [7]. In addition, a "colossal" proximity effect (CPE) was reported on underdoped YBa 2 Cu 3 O 6+x over large distances [8].In this paper, the competition between two ordered states in the presence of quenched disorder is investigated. These states are assumed sufficiently "different" that their low-T transition in the clean limit has firstorder characteristics. The approach has similarities with the classical work of Imry and Ma [9]. From the general considerations, doped TMOs are here considered, with intrinsic disorder caused by chemical substitution. For Mn-oxides, a possible rationalization of the CMR effect is discussed, with predictions including a scale T * for cluster formation -the analog of the Griffiths temperature [10] but in the regime of competing orders. For underdoped Cu-oxides, a similar inhomogeneous picture is proposed. The calculations are mainly carried out using a two dimensional (2D) toy model of Ising spins, but ...

Computational studies of models for manganese oxides show the generation of large coexisting metallic and insulating clusters with equal electronic density, in agreement with the recently discovered micrometer-sized inhomogeneities in manganites. The clusters are induced by disorder on exchange and hopping amplitudes near first-order transitions of the nondisordered strongly coupled system. The random-field Ising model illustrates the qualitative aspects of our results. Percolative characteristics are natural in this context. The conclusions are general and apply to a variety of compounds.

The resistivity rho(dc) of manganites is studied using a random resistor-network, based on phase separation between metallic and insulating domains. When percolation occurs, both as chemical composition or temperature vary, results in good agreement with experiments are obtained. Similar conclusions are reached using quantum calculations and microscopic considerations. Above the Curie temperature, it is argued that ferromagnetic clusters should exist in Mn oxides. Small magnetic fields induce large rho(dc) changes and a bad-metal state with (disconnected) insulating domains.