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Journal ArticleDOI

Random-Field Instability of the Ordered State of Continuous Symmetry

24 Nov 1975-Physical Review Letters (American Physical Society)-Vol. 35, Iss: 21, pp 1399-1401
TL;DR: In this article, it was shown that when the order parameter has a continuous symmetry, the ordered state is unstable against an arbitrarily weak random field in less than four dimensions and the borderline dimensionality above which mean-field-theory results hold is six.
Abstract: Phase transitions are considered in systems where the field conjugate to the order parameter is static and random. It is demonstrated that when the order parameter has a continuous symmetry, the ordered state is unstable against an arbitrarily weak random field in less than four dimensions. The borderline dimensionality above which mean-field-theory results hold is six. (auth)
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Journal ArticleDOI
TL;DR: In this article, the most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned, and a review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data.
Abstract: This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

3,926 citations

Journal ArticleDOI
TL;DR: In this paper, a large variety of experiments reviewed in detail here contain results compatible with the theoretical predictions, including phase diagrams of manganite models, the stabilization of the charge/orbital/spin ordered half-doped correlated electronics (CE)-states, the importance of the naively small Heisenberg coupling among localized spins, the setup of accurate mean-field approximations, and the existence of a new temperature scale T∗ where clusters start forming above the Curie temperature, the presence of stripes in the system, and many others.

2,927 citations

Journal ArticleDOI
TL;DR: A wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, $k$-core percolations, phenomena near epidemic thresholds, condensation transitions,critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks are mentioned.
Abstract: The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, important steps have been made toward understanding the qualitatively new critical phenomena in complex networks. The results, concepts, and methods of this rapidly developing field are reviewed. Two closely related classes of these critical phenomena are considered, namely, structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. Systems where a network and interacting agents on it influence each other are also discussed. A wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, $k$-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks are mentioned. Strong finite-size effects in these systems and open problems and perspectives are also discussed.

1,996 citations


Cites background from "Random-Field Instability of the Ord..."

  • ...The random-field Ising model is probably one of the simplest models showing a dramatic influence of a quenched disorder (random fields) on a collective behavior of a system with an exchange interaction (Imry and Ma, 1975; Lacour-Gayet and Toulouse, 1974)....

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Journal ArticleDOI
TL;DR: In this article, the lattice dynamics and the peculiar dielectric relaxation in relaxors are discussed, and theoretical models for the mechanisms of PNR formation and freezing into nonergodic glassy state are also presented.
Abstract: Relaxor ferroelectrics were discovered almost 50 years ago among the complex oxides with perovskite structure. In recent years this field of research has experienced a revival of interest. In this paper we review the progress achieved. We consider the crystal structure including quenched compositional disorder and polar nanoregions (PNR), the phase transitions including compositional order-disorder transition, transition to nonergodic (probably spherical cluster glass) state and to ferroelectric phase. We discuss the lattice dynamics and the peculiar (especially dielectric) relaxation in relaxors. Modern theoretical models for the mechanisms of PNR formation and freezing into nonergodic glassy state are also presented.

1,784 citations

Journal ArticleDOI
TL;DR: The phenomenology of exchange bias and related effects in nanostructures is reviewed in this paper, where the main applications of exchange biased nanostructure are summarized and the implications of the nanometer dimensions on some of the existing exchange bias theories are briefly discussed.

1,721 citations