title: Leaf-excluded percolation in two and three dimensions.
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.
authors.affiliation: School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia.
authors.forename: Zongzheng
authors.initials: Z
authors.lastname: Zhou
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Xiao
authors.initials: X
authors.lastname: Xu
authors.affiliation: School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia.
authors.forename: Timothy M
authors.initials: TM
authors.lastname: Garoni
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Youjin
authors.initials: Y
authors.lastname: Deng