Scaling in biased random walks

J. W. Halley, H. Nakanishi, R. Sundararajan

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We discuss the scaling of the statistics of a biased random walk. In the well-known model, a walk has probability p per step of stepping away from the direction of its last step. For a walk of N steps, such chains have persistence lengths p-1. We are interested in the crossover from straight-chain to random-walk behavior in the neighborhood of the point p=0, N-1=0. A scaling function has been computed for the problem of a random walk which avoids immediate returns by Schroll et al. Here we consider the self-avoiding case. A simple argument suggests a scaling function with crossover exponent 1. We present a proof that the crossover exponent is indeed one and numerical results for the scaling function on the square lattice which are consistent with this value. We also present a spin model which is asymptotically equivalent to the biased self-avoiding walk on the square lattice.

Original languageEnglish (US)
Pages (from-to)293-298
Number of pages6
JournalPhysical Review B
Issue number1
StatePublished - Jan 1 1985


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