Dynamics of bootstrap percolation

TL;DR

This paper investigates the nature of bootstrap percolation transitions, analyzing avalanche behaviors on a Bethe lattice to distinguish between first order, second order, and mixed transitions through analytical and numerical methods.

Contribution

It provides a detailed analytical and numerical analysis of avalanche distributions in bootstrap percolation, clarifying the characteristics of different transition types.

Findings

Mixed transitions show power law avalanches.

Continuous transitions exhibit truncated avalanches.

Avalanche distributions explain transition behaviors.

Abstract

Bootstrap percolation transition may be first order or second order, or it may have a mixed character where a first order drop in the order parameter is preceded by critical fluctuations. Recent studies have indicated that the mixed transition is characterized by power law avalanches, while the continuous transition is characterized by truncated avalanches in a related sequential bootstrap process. We explain this behavior on the basis of a through analytical and numerical study of the avalanche distributions on a Bethe lattice.