Generalized atmospheric Rosenbluth methods (GARM)

We show that the classical Rosenbluth method for sampling self-avoiding walks (Hammersley and Morton 1954 J. R. Stat. Soc. B 16 23, Rosenbluth and Rosenbluth 1955 J. Chem. Phys. 23 356) can be extended to a general algorithm for sampling many families of objects, including self-avoiding polygons. The implementation relies on an elementary move which is a generalization of kinetic growth; rather than only appending edges to the endpoint, edges may be inserted at any vertex provided the resulting objects still lie within the same family. This gives, for the first time, a kinetic growth algorithm for sampling self-avoiding polygons. We implement this method using pruning and enrichment (Grassberger 1997 Phys. Rev. E 56 3682) to sample self-avoiding walks and polygons. The algorithm can be further extended by mixing it with length-preserving moves, such as pivots and crank-shaft moves.