Calculation of the persistence length of a flexible polymer chain with short-range self-repulsion

For a self-repelling polymer chain consisting of n segments we calculate the persistence length L (j,n), defined as the projection of the end-to-end vector on the direction of the j-th segment. This quantity shows some pronounced variation along the chain. Using the renormalization group and epsilon-expansion we establish the scaling form and calculate the scaling function to order epsilon 2. Asymptotically, the simple result L (j,n) approximately const [j(n-j)/n]2nu-1 emerges for dimension d = 3. Also away from the excluded-volume limit L (j,n) is found to behave very similar to the swelling factor of a chain of length j (n-j)/n. We carry through simulations which are found to be in good accord with our analytical results. For d = 2 both our and previous simulations as well as theoretical arguments suggest the existence of logarithmic anomalies.