Swelling-collapse transition of self-attracting walks

A Ordemann; G Berkolaiko; S Havlin; A Bunde

doi:10.1103/physreve.61.r1005

Swelling-collapse transition of self-attracting walks

Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Feb;61(2):R1005-7. doi: 10.1103/physreve.61.r1005.

Authors

A Ordemann¹, G Berkolaiko, S Havlin, A Bunde

Affiliation

¹ Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel and Institut fur Theoretische Physik III, Justus-Liebig-Universitat Giessen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany.

PMID: 11046524
DOI: 10.1103/physreve.61.r1005

Abstract

We study the structural properties of self-attracting walks in d dimensions using scaling arguments and Monte Carlo simulations. We find evidence of a transition analogous to the Theta transition of polymers. Above a critical attractive interaction u(c), the walk collapses and the exponents nu and k, characterizing the scaling with time t of the mean square end-to-end distance <R2> approximately t(2nu) and the average number of visited sites <S> approximately t(k), are universal and given by nu=1/(d+1) and k=d/(d+1). Below u(c), the walk swells and the exponents are as with no interaction, i.e., nu=1/2 for all d, k=1/2 for d=1 and k=1 for d>/=2. At u(c), the exponents are found to be in a different universality class.