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Griffiths Singularities and the Dynamics of Random Systems

  • A. J. Bray
Part of the Springer Series in Synergetics book series (SSSYN, volume 43)

Abstract

Two decades ago Griffiths [1] showed that the free energy F of a diluted ferromagnet is non-analytic as a function of the applied magnetic field h, at h = 0, at all temperatures T below the critical point T c (1) of the undiluted system. This singularity in F(h) at h = 0 has since been termed a ‘Griffiths singularity’. Its physical origin is the presence in the diluted system of arbitrarily large regions which locally resemble a system below its ordering temperature. Such regions occur due to random statistical fluctuations in the quenched disorder. Subsequently, the concept of Griffiths singularities has been extended [2,3] to more general kinds of quenched disorder than simple dilution.

Keywords

Steep Descent Percolation Cluster Cayley Tree Random System Eigenvalue Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • A. J. Bray
    • 1
  1. 1.Department of Theoretical PhysicsUniversity of ManchesterManchesterUK

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