2017/08/10 by Peter Grassberger · 1 citation
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.119.140601
published as Phys. Rev. Lett. 119, 140601 (2017) · 5 pages main paper + 5 pages supplementary material
arxiv created 2017/08/10 · arxiv updated 2017/10/11
Although the title seems self-contradictory, it does not contain a misprint. The model we study is a seemingly minor modification of the "true self-avoiding walk" (TSAW) model of Amit, Parisi, and Peliti in two dimensions. The walks in it are self-repelling up to a characteristic time T^* (which depends on various parameters), but spontaneously (i.e., without changing any control parameter) become self-trapping after that. For free walks, T^* is astronomically large, but on finite lattices the transition is easily observable. In the self-trapped regime, walks are subdiffusive and intermittent, spending longer and longer times in small areas until they escape and move rapidly to a new area. In spite of this, these walks are extremely efficient in covering finite lattices, as measured by average cover times.