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Adsorbing and Collapsing Directed Animals

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Abstract

A model of a self-interacting directed animal, which also interacts with a solid wall, is studied as a model of a directed branched polymer which can undergo both a collapse and an adsorption transition. The directed animal is confined to a 45° wedge, and it interacts with one of the walls of this wedge. The existence of a thermodynamic limit in this model shown, and the presence of an adsorption transition is demonstrated by using constructive techniques. By comparing this model to a process of directed percolation, we show that there is also a collapse or θ-transition in this model. We examine directed percolation in a wedge to show that there is a collapse phase present for arbitrary large values of the adsorption activity. The generating function of adsorbing directed animals in a half-space is found next from which we find the tricritical exponents associated with the adsorption transition. A full solution for a collapsing directed animal seems intractible, so instead we examine the collapse transition of a model of column convex directed animals with a contact activity next.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

    E. J. Janse van Rensburg & A. Rechnitzer

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  1. E. J. Janse van Rensburg
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  2. A. Rechnitzer
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van Rensburg, E.J.J., Rechnitzer, A. Adsorbing and Collapsing Directed Animals. Journal of Statistical Physics 105, 49–91 (2001). https://doi.org/10.1023/A:1012225909169

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