Scaling of Star Polymers with one to 80 Arms

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 gamma(f). For completeness we made also extensive simulations of linear (unbranched) polymers which give the best estimates for the exponent gamma