Dynamic critical behavior of an extended reptation dynamics for self-avoiding walks

We consider lattice self-avoiding walks and discuss the dynamic critical behavior of two dynamics that use local and bilocal moves and generalize the usual reptation dynamics. We determine the integrated and exponential autocorrelation times for several observables, perform a dynamic finite-size scaling study of the autocorrelation functions, and compute the associated dynamic critical exponents z. For the variables that describe the size of the walks, in the absence of interactions we find $z\approx 2.2$ in two dimensions and $z\approx 2.1$ in three dimensions. At the $\theta$ point in two dimensions we have $z\approx \mathrm{2.3.}$