Abstract
We solve a model of self-avoiding walks which allows for a site to be visited up to two times by the walk on the Husimi lattice. This model is inspired in the Domb-Joyce model and was proposed to describe the collapse transition of polymers with one-site interactions only. We consider the version in which immediate self-reversals of the walk are forbidden. The phase diagram we obtain for the grand-canonical version of the model is similar to the one found in the solution of the Bethe lattice, with two distinct polymerized phases: a tricritical point and a critical endpoint.
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