The nontriviality of the one-dimensional problem of a 'true' self-avoiding walk

Abstract

It is shown that the root-mean-square distance R2(12)/ for the self-avoiding walk problem is related to the number of steps N as R2 approximately N2 nu with nu =2/3 rather than the 'self-obvious' nu =1. This coincides with the mean-field theory result obtained by Pietronero (1983) which erroneously was not extended to the case d=1.