Leaf-excluded percolation in two and three dimensions

TL;DR

This paper introduces a leaf-excluded percolation model, studies its critical properties on 2D and 3D lattices via Monte Carlo simulations, and finds it belongs to the standard percolation universality class.

Contribution

The paper presents the first study of leaf-excluded percolation, providing precise critical thresholds and confirming its universality class through simulation.

Findings

Critical threshold on square lattice: 0.3552475(8)

Critical threshold on simple-cubic lattice: 0.185022(3)

Phase transition belongs to standard percolation universality class

Abstract

We introduce the \emph{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 $0.355\,247\,5(8)$ (square) and $0.185\,022(3)$ (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.