We compute the exact root-mean-square end-to-end distance of the interacting self-avoiding walk (ISAW) up to 27 steps on the simple cubic lattice. These data are used to construct a fixed point equation to estimate the theta temperature of the collapse transition of the ISAW. With the Bulirsch-Stoer extrapolation method, we obtain accurate results that can be compared with large-scale long-chain simulations. The free parameter ω in extrapolation is precisely determined using a parity property of the ISAW. The systematic improvement of this approach is feasible by adopting the combination of exact enumeration and multicanonical simulations.
Keywords: Bulirsch–Stoer extrapolation; collapse transition; exact enumeration; interacting self-avoiding walks.