Abstract

Two new models of anisotropic spiral self-avoiding loops on the square lattice are considered. These models are closely related to the models of anisotropic spiral self-avoiding walks, which are recently proposed by Manna, (1984). The generating function for the number Un of anisotropic spiral self-avoiding loops with n steps is derived for each model. It is shown that the asymptotic form of Un (n must be even) is n-1/2 mu n where mu is the connective constant of the corresponding Manna model.

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