Griffiths Singularities and the Dynamics of Random Systems

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


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.


Steep Descent Percolation Cluster Cayley Tree Random System Eigenvalue Spectrum 
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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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