Leaf-excluded percolation in two and three dimensions

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.