de Menezes M A, Moukarzel C F
Instituto de Física, Universidade Federal Fluminense, CEP 24210-340, Niteroi, RJ, Brazil.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Nov;60(5 Pt B):5699-705. doi: 10.1103/physreve.60.5699.
We study directed rigidity percolation (equivalent to directed bootstrap percolation) on three different lattices: square, triangular, and augmented triangular. The first two of these display a first-order transition at p=1, while the augmented triangular lattice shows a continuous transition at a nontrivial p(c). On the augmented triangular lattice we find, by extensive numerical simulation, that the the directed rigidity percolation transition belongs to the same universality class as the directed percolation. The same conclusion is reached by studying its surface critical behavior, i.e., the spreading of rigidity from finite clusters close to a nonrigid wall. Near the discontinuous transition at p=1 on the triangular lattice, we are able to calculate the finite-size behavior of the density of rigid sites analytically. Our results are confirmed by numerical simulation.
我们研究了三种不同晶格上的定向刚性渗流（等同于定向自引导渗流）：正方形晶格、三角形晶格和增强三角形晶格。其中前两种晶格在(p = 1)时呈现一阶相变，而增强三角形晶格在非平凡的(p(c))处呈现连续相变。通过广泛的数值模拟，我们发现在增强三角形晶格上，定向刚性渗流相变与定向渗流属于同一普适类。通过研究其表面临界行为，即刚性从靠近非刚性壁的有限团簇的扩展，也得出了相同的结论。在三角形晶格上(p = 1)处的不连续相变附近，我们能够解析计算刚性位点密度的有限尺寸行为。我们的结果通过数值模拟得到了证实。
