Leaf-excluded percolation in two and three dimensions

Zongzheng Zhou, Xiao Xu, Tim Garoni, Youjin Deng

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Abstract

We introduce the leaf-excluded percolation model, which corresponds to independent bond percolation conditioned on the absence of leaves (vertices of degree one). We study the leaf-excluded model on the square and simple-cubic lattices via Monte Carlo simulation, using a worm-like algorithm. By studying wrapping probabilities, we precisely estimate the critical thresholds to be 0.3552475(8) (square) and 0.185022(3) (simple-cubic). Our estimates for the thermal and magnetic exponents are consistent with those for percolation, implying that the phase transition of the leaf-excluded model belongs to the standard percolation universality class.
Original languageEnglish
Article number022140
Pages (from-to)1-6
Number of pages6
JournalPhysical Review E
Volume91
Issue number2
DOIs
Publication statusPublished - 2015

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