Two-dimensional copolymers and multifractality: Comparing perturbative expansions, Monte Carlo simulations, and exact results
Abstract
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.
- Publication:
-
Physical Review E
- Pub Date:
- April 2002
- DOI:
- 10.1103/PhysRevE.65.042801
- arXiv:
- arXiv:cond-mat/0203504
- Bibcode:
- 2002PhRvE..65d2801V
- Keywords:
-
- 61.41.+e;
- 64.60.Ak;
- 64.60.Fr;
- 11.10.Gh;
- Polymers elastomers and plastics;
- Renormalization-group fractal and percolation studies of phase transitions;
- Equilibrium properties near critical points critical exponents;
- Renormalization;
- Condensed Matter - Soft Condensed Matter
- E-Print:
- 5 pages