Selective bootstrap percolation

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.

Cooperative transport with selective kinetic constraints

“…In this paper we investigate a more general family of cooperative exclusion processes in which the number of vacant neighbours required for hopping is not determined by a minimum threshold but rather can be any specific set of non-negative integers (lower than lattice coordination number). This idea of selective kinetic constraints has been recently introduced in the context of bootstrap percolation to provide models of multiple hybrid phase transitions in a fully homogeneous environment [17]. We are primarily interested here in the emergence of complex convexity-change density profiles and dynamical effective particle attraction or repulsion generated by the subtle interplay of nonequilibrium fluxes and kinetic constraints, in the absence of any static interaction (apart from hard-core exclusion).…”