A generalised self-avoiding walk

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Abstract
The authors study a generalised self-avoiding walk on a lattice in which each vertex may be visited less than k time. Turban (1983) has argued that, for this model, the critical exponents should change continuously with k from the standard self-avoiding walk exponents (k=2) to mean-field exponents. By generating series expansions for both two- and three-dimensional lattices, the authors find strong support for the conventional, and opposing, view that the critical exponents remain unchanged for finite k, only taking on their mean-field values in the limit k to infinity .

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