A Potts/Ising correspondence on Thin Graphs

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Abstract

We note that it is possible to construct a bond vertex model that displays q-state Potts criticality on an ensemble of f3 random graphs of arbitrary topology, which we denote as 'thin' random graphs in contrast to the fat graphs of the planar diagram expansion. Since the four-vertex model in question also serves to describe the critical behaviour of the Ising model in field, the formulation reveals an isomorphism between the Potts and Ising models on thin random graphs. On planar graphs a similar correspondence is present only for q = 1, the value associated with percolation.

Original languageEnglish
Pages (from-to)5029-5036
Number of pages8
JournalJournal of Physics A: Mathematical and General
Volume32
Issue number27
DOIs
Publication statusPublished - 9 Jul 1999

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