# Newman-Ziff algorithm for the bootstrap percolation: application to the Archimedean lattices

## TL;DR

This paper introduces efficient algorithms based on the Newman-Ziff method to analyze bootstrap and diffusion percolation models on Archimedean lattices, revealing they share the same universality class as classical percolation.

## Contribution

The authors extend the Newman-Ziff algorithm to bootstrap and diffusion percolation, enabling high-precision calculation of thresholds and critical exponents on Archimedean lattices.

## Key findings

- Bootstrap and diffusion percolation have the same critical exponents as classical percolation.
- The algorithms allow precise determination of percolation thresholds.
- Percolation transitions are continuous in these models.

## Abstract

We propose very efficient algorithms for the bootstrap percolation and the diffusion percolation models by extending the Newman-Ziff algorithm of the classical percolation [M. E. J. Newman and R. M. Ziff, Phys. Rev. Lett. 85 (2000) 4104]. Using these algorithms and the finite-size-scaling, we calculated with high precision the percolation threshold and critical exponents in the eleven two-dimensional Archimedean lattices. We present the condition for the continuous percolation transition in the bootstrap percolation and the diffusion percolation, and show that they have the same critical exponents as the classical percolation within error bars in two dimensions. We conclude that the bootstrap percolation and the diffusion percolation almost certainly belong to the same universality class as the classical percolation.