Endless self-avoiding walks

We introduce a self-avoiding walk model for which end-effects are completely eliminated. We enumerate the number of these walks for various lattices in dimensions two and three, and use these enumerations to study the properties of this model. We find that endless self-avoiding walks have the same connective constant as self-avoiding walks, and the same Flory exponent ν. However, there is no power law correction to the exponential number growth for this new model, i.e. the critical exponent γ = 1 exactly in any dimension. In addition, the number growth has no analytic corrections to scaling, and we have convincing numerical evidence to support the conjecture that the amplitude for the number growth is a universal quantity. The technique by which end-effects are eliminated may be generalized to other models of polymers such as interacting self-avoiding walks. (paper)