Long-range correlation effects in directional living polymers.

The statistics of (equilibrium) living polymers including both linear chains and rings are considered theoretically. Particular attention is addressed to directional polymers characterized by an arrow along the backbone defined by its chemical structure. Thermodynamic and correlation properties of living polymers are studied both in the mean-field and in the critical scaling regimes. It is shown that living polymers with no rings, classical living polymers with rings, and directional living polymers with rings form three distinct classes characterized by different critical exponents and qualitatively different long-range correlation functions.