The statistical mechanics of random copolymers

Random copolymers are polymers with two or more types of monomer where the monomer sequence is determined by some random process. Once determined, the sequence is fixed so random copolymers are an example of a system with quenched randomness. We review the statistical mechanics of random copolymers, focusing on self-avoiding walk models where there are two types of monomers, A and B, which are randomly distributed along the polymer chain. Theoretical, approximate and numerical results are reviewed for models of the random copolymer adsorption, localization and collapse phase transitions. We concentrate on what is known about the existence of phase transitions, the Morita approximation, and results about self-averaging. We also discuss, in less detail, the replica trick and numerical methods including Monte Carlo methods, exact enumeration and transfer-matrix methods. Important open problems are identified throughout and highlighted in the conclusions. (topical review)