中国物理B ›› 1997, Vol. 6 ›› Issue (4): 257-265.doi: 10.1088/1004-423X/6/4/003
秦勇1, 杨展如2, 林振权3
LIN ZHEN-QUAN (林振权)ab, YANG ZHAN-RU (杨展如)bc, QIN YONG (秦勇)b
摘要: The critical behaviors of bond percolation on a family of Sierpinski carpets (SCs) are studied. We distinguish two sorts of bonds and assign them to two kinds of occupation probabilities. We develop the usual choice of cell on translationally invariant lattices and choose suitable cells to cover the fractal lattice. On this basis we construct a new real-space renormalization group (RG) transformation scheme and use it to solve the percolation problems. Phase transitions of percolation on such fractals with infinite order of ramification are found at non-trivial bond occupation probabilities. The percolation threshold values, correlation length exponents ν, and the RG flow diagrams are obtained. The flow diagrams are remarkably similar to those of Ising model and Potts model. This agrees with the correspondence between the pure bond percolation and Potts model.
中图分类号: (Lattice theory and statistics)