Griffiths Singularities and the Dynamics of Random Systems
Two decades ago Griffiths  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.
KeywordsSteep Descent Percolation Cluster Cayley Tree Random System Eigenvalue Spectrum
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