Novel Superuniversal Behavior of a Random-Walk Model

A model of interacting random walks is proposed in which each new site visited has a weight factor $p$. For $1<~p<~\infty$, the model interpolates between purely random walks and self-avoiding walks. When $0<p<\mathrm{}1\mathrm{}$, the model describes attracting random walks (and also noninteracting random walks on a lattice with static traps), and shares some of the intriguing features of random walks on percolation fractals—e.g, dimension-independent exponents.