晶格动物在上临界尺寸的标度行为
Scaling behaviour of lattice animals at the upper critical dimension
摘要：
我们进行数值模拟的格子动物问题在上临界尺寸d=8的超立方晶格，以调查对数校正缩放。我们的随机抽样方法是基于修剪丰富的Rosenbluth方法（PERM），适合线性聚合物，并产生高的统计数据与动物组成的多达8000个网站。我们估计分区和（不同动物的数量）和回转半径。我们重新验证了巴黎Sourlas预测的领先指数，并比较两个部分不同的预测集从文献中的几何校正指数。最后，我们提出了一个新的巴黎Sourlas型标度关系，并测试，适当的湍流修正指数。
英文摘要：
We perform numerical simulations of the lattice-animal problem at the upper critical dimension d=8 on hypercubic lattices in order to investigate logarithmic corrections to scaling there. Our stochastic sampling method is based on the pruned-enriched Rosenbluth method (PERM), appropriate to linear polymers, and yields high statistics with animals comprised of up to 8000 sites. We estimate both the partition sums (number of different animals) and the radii of gyration. We re-verify the Parisi-Sourlas prediction for the leading exponents and compare the logarithmic-correction exponents to two partially differing sets of predictions from the literature. Finally, we propose, and test, a new Parisi-Sourlas-type scaling relation appropriate for the logarithmic-correction exponents.
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