Upper bounds on cluster distribution functions and the nature of the Griffiths singularity

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Abstract

An upper bound is obtained on the number of N-site clusters. This bound enables to show that the free energy of a quenched random classical system of spins interacting via short-range interactions is differentiable to all orders in the magnetic field below some finite occupation probability. It follows that at low occupation probabilities, the Griffiths singularity is an essential singularity.

Original languageEnglish
Pages (from-to)2364-2366
Number of pages3
JournalPhysical Review B-Condensed Matter
Volume18
Issue number5
DOIs
StatePublished - 1978

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