2003/07/31 by Lothar Schäfer, Knut Elsner, Klaus Elsner · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1140/epje/i2003-10071-1
28 pages, 8 figures, changed content
arxiv created 2003/11/17 · openalex publication_date 2004/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 epsilon2. Asymptotically the simple result L(j,n) ~ const(j(n-j)/n)^(2nu-1) emerges for dimension d=3. Also outside 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.