Scaling of Star Polymers with 1−80 Arms

This is the authors' abstract. We don't add key points for this paper.

We present large statistics simulations of 3-dimensional star polymers with up to f = 80 arms and with up to 4000 monomers per arm for small values of f . They were done for the Domb−Joyce model on the simple cubic lattice. This is a model with soft core exclusion which allows multiple occupancy of sites but punishes each same-site pair of monomers with a Boltzmann factor v < 1. We use this to allow all arms to be attached at the central site, and we use the “magic” value v = 0.6 to minimize corrections to scaling. The simulations are made with a very efficient chain growth algorithm with resampling, PERM, modified to allow simultaneous growth of all arms. This allows us to measure not only the swelling (as observed from the center-to-end distances) but also the partition sum. The latter gives very precise estimates of the critical exponents γ f . For completeness we made also extensive simulations of linear (unbranched) polymers which give the best estimates for the exponent γ.