- 作者: Chin-Kun Hu
- 中文摘要: Many problems in mathematics, physical sciences, and life sciences can be described by percolation models. In this paper, we review our recent work in universal quantities and universal finite-size scaling functions (UFSSF's) of percolation models. The quantities we consider include the existence probability (also called the spanning probability), Ep, the percolation probability, P, and the probability of the appearance of n percolating clusters, Wn. The topics under discussion include: (1) boundary conditions, aspect ratios, and finite-size scaling functions; (2) UFSSF's of Ep and P in lattice percolation models; (3) UFSSF's of Wn in lattice percolation models; (4) UFSSF? of Ep and Wn in continuum percolation models; (5) UFSSF's of the q-state bond-correlated percolation model and q-state Potts model without nonuniversal metric factors; and (6) boundary conditions and the average number of percolating clusters. Some other related developments and problems for further research are also discussed.
- 英文摘要: --
- 中文關鍵字: percolation, critical phenomena, finite-size scaling, universality
- 英文關鍵字: --