期刊:Physical Review A [American Physical Society] 日期:1992-10-01卷期号:46 (8): 4471-4474被引量:33
标识
DOI:10.1103/physreva.46.r4471
摘要
We describe the results of an analytical and numerical study of the geometrical properties of random spanning trees on a square lattice. We determine exactly the probability distribution of the coordination number at a site on a random spanning tree. We argue that the probability that s sites get disconnected from the tree on deleting a bond at random from the tree varies as ${\mathit{s}}^{\mathrm{\ensuremath{-}}11/8}$ for large s. The probability that a loop of perimeter l is formed on adding an additional link at random varies as ${\mathit{l}}^{\mathrm{\ensuremath{-}}8/5}$ for large l. These distributions are also determined numerically in a Monte Carlo simulation on random spanning trees generated by using Broder's algorithm. The numerical results are in complete agreement with the theoretical predictions.