Heriot-Watt Mathematics Report Series
HWM99-1, 13 Jan 1999
A Potts/Ising correspondence on Thin Graphs
D A Johnston
Abstract
We note that it is
possible to construct a bond vertex model
which displays q-state Potts criticality
on an ensemble of phi3 random graphs
of arbitrary topology (``thin'' random graphs).
Since the four vertex model in question
also serves to describe the critical behaviour
of the Ising model in field,
the formulation reveals a surprising isomorphism between the Potts
and Ising models on thin random graphs.
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