"True" self-avoiding walk in one dimension

Abstract

The true self-avoiding walk in one dimension is studied via extensive Monte Carlo simulations. For any finite and nonzero value of the repulsion parameter $g$, the asymptotic behavior of the end-to-end distance is characterized by a universal exponent $\ensuremath{\nu}=0.67\ifmmode\pm\else\textpm\fi{}0.01$, in close agreement with the value $\ensuremath{\nu}=\frac{2}{3}$ recently predicted by one of us (L.P.).