Selective Bootstrap Percolation

TL;DR

This paper introduces a new class of bootstrap percolation models with selective culling, revealing multiple hybrid phase transitions on a Bethe lattice, and suggests applications to glass transition modeling.

Contribution

It proposes a novel selective culling bootstrap percolation model that exhibits multiple phase transitions, extending to facilitation dynamics and complex cooperative systems.

Findings

Multiple hybrid phase transitions observed on Bethe lattice.

Selective culling induces complex phase behavior in homogeneous systems.

Potential applications to glass and cooperative dynamics models.

Abstract

A new class of bootstrap percolation models in which particle culling occurs only for certain numbers of nearest neighbours is introduced and studied on a Bethe lattice. Upon increasing the density of initial configuration they undergo multiple hybrid (or mixed-order) phase transitions, showing that such intriguing phase behaviours may also appear in fully homogeneous situations/environments, provided that culling is selective rather than cumulative. The idea immediately extends to facilitation dynamics, suggesting a simple way to construct one-component models of multiple glasses and glass-glass transitions as well as more general coarse-grained models of complex cooperative dynamics.