Structural properties of self-attracting walks

A. Ordemann, E. Tomer, G. Berkolaiko, S. Havlin, A. Bunde

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Self-attracting walks (SATW) with attractive interaction [formula presented] display a swelling-collapse transition at a critical [formula presented] for dimensions [formula presented] analogous to the [formula presented] transition of polymers. We are interested in the structure of the clusters generated by SATW below [formula presented] (swollen walk), above [formula presented] (collapsed walk), and at [formula presented] which can be characterized by the fractal dimensions of the clusters [formula presented] and their interface [formula presented] Using scaling arguments and Monte Carlo simulations, we find that for [formula presented] the structures are in the universality class of clusters generated by simple random walks. For [formula presented] the clusters are compact, i.e., [formula presented] and [formula presented] At [formula presented] the SATW is in a new universality class. The clusters are compact in both [formula presented] and [formula presented] but their interface is fractal: [formula presented] and [formula presented] in [formula presented] and [formula presented] respectively. In [formula presented] where the walk is collapsed for all u and no swelling-collapse transition exists, we derive analytical expressions for the average number of visited sites [formula presented] and the mean time [formula presented] to visit S sites.

Original languageEnglish
Pages (from-to)9
Number of pages1
JournalPhysical Review E
Issue number4
StatePublished - 2001


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