Rectangular renormalization. (English) Zbl 0868.60106
Summary: A generalized real-space renormalization scheme is developed for geometrical critical phenomena. The renormalization group is parametrized by the standard length-scaling factor and a new rectangular area-fraction factor. This rectangular renormalization scheme utilizes relatively small rectangular sublattices to effectively renormalize large square lattices. With the area-fraction factor, one can systematically study rectangular generalizations of the conventional square-cell renormalization theories. Application to self-avoiding random walks yields critical descriptors that are comparable to, and in most cases better than previous results obtained from more complex renormalization schemes.
MSC:
60K40 | Other physical applications of random processes |
82B28 | Renormalization group methods in equilibrium statistical mechanics |
82B27 | Critical phenomena in equilibrium statistical mechanics |