Recent developments in Monte Carlo Simulations of lattice models for polymer systems

A brief review is given of methodological advances made during the past decade with the Monte Carlo sampling of equilibrium properties of simple lattice models of polymer systems, and representative applications of these new algorithms are summarized. These algorithms include Wang-Landau (WL) sampling, the pruned-enriched Rosenbluth method (PERM), and topology violating dynamic Monte Carlo algorithms such as combinations of,local moves, slithering snake moves, and "double bridging" moves for the bond fluctuation model. The applications mentioned concern phase-transition-like phenomena of single chains (collapse and crystallization in bad solvents; interplay of collapse and adsorption; escape of chains from confining tubes; microphase separation in binary bottle brushes) and nontrivial correlation effects in dense systems of many chains (intramolecular long-range correlations in melts; fluctuation effects of micelles in homopolymer-block copolymer blends.) While all these examples refer to work on lattice models, these algorithms are useful for off-lattice models as well. Open problems and directions for future work are briefly addressed.