Kinetic-growth self-avoiding walks on small-world networks
Instituto de Ciencia de Materiales, Consejo Superior de Investigaciones Científicas (CSIC), Campus de Cantoblanco, 28049 Madrid, Spain
Corresponding author: a firstname.lastname@example.org
Published online: 28 March 2007
Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz small-world networks, rewired from a two-dimensional square lattice. The maximum length L of this kind of walks is limited in regular lattices by an attrition effect, which gives finite values for its mean value 〈L 〉. For random networks, this mean attrition length 〈L 〉 scales as a power of the network size, and diverges in the thermodynamic limit (system size N ↦∞). For small-world networks, we find a behavior that interpolates between those corresponding to regular lattices and randon networks, for rewiring probability p ranging from 0 to 1. For p < 1, the mean self-intersection and attrition length of kinetically-grown walks are finite. For p = 1, 〈L 〉 grows with system size as N1/2, diverging in the thermodynamic limit. In this limit and close to p = 1, the mean attrition length diverges as (1-p)-4. Results of approximate probabilistic calculations agree well with those derived from numerical simulations.
PACS: 89.75.Fb – Structures and organization in complex systems / 89.75.Hc – Networks and genealogical trees / 87.23.Ge – Dynamics of social systems / 05.40.Fb – Random walks and Levy flights
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007