Two-dimensional copolymers and multifractality: Comparing perturbative expansions, Monte Carlo simulations, and exact results

We analyze the scaling laws for a set of two different species of long flexible polymer chains joined together at one of their extremities (copolymer stars) in space dimension D=2. We use a formerly constructed field-theoretic description and compare our perturbative results for the scaling exponents with recent conjectures for exact conformal scaling dimensions derived by a conformal invariance technique in the context of D=2 quantum gravity. A simple Monte Carlo simulation brings about reasonable agreement with both approaches. We analyze the remarkable multifractal properties of the spectrum of scaling exponents.