Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volume 33, Issue 5, Pages 929-943Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0305-4470/33/5/309
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The q-state Ports model on a Cayley tree can be solved by a recursion formula depending on the properties at the surface. The model on a Bethe lattice is obtained by extrapolating the interior of a Cayley tree sufficiently far from the surface in order to have a stable fixed point of the recursion. For q > 2 we find a second-order transition of percolation type at the Bethe-Peierls temperature and a first-order transition at a higher temperature. For coordination number z = 3 the recursion extrapolated to q = 1 is identical to the logistic equation. The Feigenbaum route to chaos appears for antiferromagnetic coupling of the Ports model. The first period doubling corresponds to a multicritical point in the phase diagram of the Ports model.
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