DIRECTED COMPACT PERCOLATION - CLUSTER SIZE AND HYPERSCALING
DIRECTED COMPACT PERCOLATION - CLUSTER SIZE AND HYPERSCALING
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DOI：
10.1088/0305-4470/22/22/020
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发表时间：
1989-11-21
期刊：
影响因子：
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通讯作者：
ESSAM, JW
中科院分区：
文献类型：
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作者：
ESSAM, JW
获得了方晶格上紧凑定向渗流簇的长度和尺寸分布的精确递推关系。长度分布的矩生成函数的对应关系以封闭形式获得，而在尺寸分布的情况下，仅获得前三个矩。这项工作是针对从各向异性晶格上任意宽度的种子生长的簇进行的。结果表明存在对偶性，它将临界曲线两侧的矩生成函数联系起来。两种分布的矩都具有满足恒定间隙假设的临界指数，其中间隙指数 nu = 2 和 Delta = 3 分别对应于缩放长度和缩放大小。定向渗透的常见超尺度关系被发现对于紧凑簇无效，并被替换为 Delta= nu+ D nu 垂直于 其中 nu 垂直于 是对应于簇宽度的指数，D 是横向维度的数量（对于方形晶格 = 1）。
Exact recurrence relations are obtained for the length and size distributions of compact directed percolation clusters on the square lattice. The corresponding relation for the moment generating function of the length distribution is obtained in closed form whereas in the case of the size distribution only the first three moments are obtained. The work is carried out for clusters grown from a seed of arbitrary width on an anisotropic lattice. A duality property is shown to exist which relates the moment generating functions on the two sides of the critical curve. The moments of both distributions have critical exponents which satisfy a constant gap hypothesis with gap exponents nu= 2 and Delta= 3 corresponding to the scaling length and scaling size respectively. The usual hyperscaling relation for directed percolation is found to be invalid for compact clusters and is replaced by Delta= nu+ D nu perpendicular to where nu perpendicular to is the exponent corresponding to the cluster width and D is the number of transverse dimensions (= 1 for the square lattice).