The cluster structure in collapsing animals

Published under licence by IOP Publishing Ltd
, , Citation E J Janse van Rensburg 2000 J. Phys. A: Math. Gen. 33 3653 DOI 10.1088/0305-4470/33/19/303

0305-4470/33/19/3653

Abstract

In this paper I revisit the connection between edge percolation and the collapse transition in lattice animals. It was shown by Domb (1976 J. Phys. A: Math. Gen. 9 L141) that the critical percolation point is a θ-transition in a certain model of self-interacting animals. I extend this result by showing that the free energy of lattice animals in the cycle-contact model is non-analytic in contact- and cycle-activities at points other than the critical percolation point. This correspondence between percolation and collapsing animals suggests that the collapse transition in this model may be related to percolation. Contact-collapse in animals is then studied from a percolation of clusters of contacts perspective. I first argue that there is a critical activity for percolation of clusters of contacts, and then investigate this numerically.

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10.1088/0305-4470/33/19/303