Scaling Exponents for a Monkey on a Tree: Fractal Dimensions of Randomly Branched Polymers

We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large, randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase and the collapse transition, where loops in the polymers are irrelevant. Here the asymptotic statistics of the polymers is that of lattice trees, and diffusion on them is reminiscent of the climbing of a monkey on a tree. We calculate a set of universal scaling exponents including the diffusion exponent and the fractal dimension of the minimal path to two-loop order and, where available, compare them to numerical results.