Exact Enumeration of Self-Avoiding Walks on Percolation Clusters

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• 作者：Niklas Fricke ; Wolfhard Janke
• 关键词：Exact Enumeration ; Self-Avoiding Walks ; Percolation
• 刊名：Physics Procedia
• 出版年：2012
• 出版时间：2012
• 年：2012
• 卷：34
• 期：Complete
• 页码：39-43
• 全文大小：369 K

文摘

We study the scaling behavior of self-avoiding walks on critically dilute lattices. To this aim, we have developed a new enumeration technique, which is highly e_cient for this particular problem. It makes use of the low connectivity and the self-similar nature of the critical percolation cluster. The problem can thus be factorized, and the exponential complexity that usually a_icts exact enumeration can be avoided. This allowed us to enumerate all conformations of walks of 1000 steps for a large random sample of percolation clusters in two dimensions. The scaling exponents could thus be determined with very high precision.